School Science Lessons
26. Sound, resonance, pitch, tuning fork, oscillation, vibration
2013-01-16
Please send comments to: J.Elfick@uq.edu.au
Table of contents
26.0.0 Sound
See:
Waves and sound, School of Physics, University of New South Wales. [Animations
needs Flash 8 Plugin.]
Sound & Waves, "Prof Bunsen",
(commercial website)
4.93 Sound, experiments, UNESCO
26.8.0 Interference and diffraction
of sound
26.6.0 Musical notes, ear and voice
26.2.0 Pitch, frequency
26.7.0 Reflection and refraction
of sound
26.3.2 Resonance in air columns, musical instruments
26.3.1 Resonance in strings, musical instruments
26.9.0 Sound recording and reproduction
26.5.0 Speed of sound
26.4.0 Transmission of sound
26.3.3.3 Tuning forks
26.1.0 Wave properties of sound, sound waves,
vibrations, oscillations
26.2.0 Pitch, frequency
26.2.0 Pitch, frequency
26.1.01 Beats with two tuning forks
26.2.4 Doppler effect, change in pitch
25.14 Doppler's principle
26.2.5 Hanging buckets, change in pitch
26.2.1 Pitch and length,
26.2.2 Pitch and tension
26.2.8 Squealing balloon
26.2.9 Record player, change in pitch
26.2.7 Stretched rubber band, change in pitch
26.2.6 Thin and thick strings, change in pitch
26.2.3 Whirling pipes, pitch and length
26.3.2 Resonance in air columns, musical instruments
S01
Singing rods, resonance in an open rod
See
pdf: Singing Bowl
S04
Sound tube, Resonance tones from twirling
26.3.2.14 Blow pieces of drinking straw
2.7 Bottle sounds, (Primary)
26.3.2.7 Bottle xylophone
26.3.2.15 Bunsen burner trombone
26.3.2.12 Drinking straw oboe and trombone
26.3.7 Glass harmonica
26.3.2.13 Humming paper tube
4.96 Kazoo tube, comb kazoo, goose
horn tube
1.7 Knocking sounds, (Primary)
26.3.2.11 Pan pipes
26.3.2.8 Reed vibrations
26.3.2.6 Resonance in aluminium pipe
26.3.2.5 Resonance in paper pipe or drinking
straw
26.3.6 Slide whistle, piston flute
26.3.2.4 Timbre (quality)
26.3.2.1 Wind instruments
26.3.1 Resonance in strings, musical instruments
26.3.1.9 Monochord, sonometer, string
26.3.1.1 Paper rider thrown off vibrating string
26.3.1.8 Piano string resonance
26.3.1.10 Pitch and mass (density) of vibrating
strings
26.3.1.11 Plastic bottle guitar strings
26.3.1.2 String resonates with tuning fork
26.3.1.4 String vibrates at constant length
26.3.1.3 String vibrates at constant tension
3.12 String telephone (Primary)
26.3.1.4.1 Violin strings and piano strings
26.0.0 Sound
26.3.0.10 Aeolian harp, wind harp
26.4.4 Bell from a spoon
2.2 Bird sounds (Primary)
2.7 Bottle sounds (Primary)
26.3.0.7 Cellophane noise
26.3.0.4 Comb resonator, amplify sound from
comb, chimes
26.3.0.5 Drink-can to amplify the sound of
a thread
1.16 Hearing sounds game (Primary)
4.7 How sound travels (Primary)
26.3.0.2 Insect footsteps in a paper bag
26.3.0.9 Knocking on bottles, blowing over
bottles
1.7 Knocking sounds (Primary)
See
pdf: Light modulation, flashlight connected to iPod, MP3, CD Player
4.99 Materials that absorb sound
26.3.0.0 Resonance, standing waves (stationary
waves)
4.93 Sound experiments, UNESCO
26.9.0 Sound reproduction, microphone
2.190 Sound wave patterns
26.3.0.3 Spray from "fish wash" dishes in Chinese
temples "frictionizing" the brim, stationary waves
26.3.0.6 Tap different containers
26.3.0.1 Wine glass resonance
26.3.3.3 Tuning forks
26.3.3.3 Tuning forks
26.3.1.5 Frequency of a tuning fork with a
sonometer
26.8.2 Interference of sound waves
with tuning forks
26.8.6 Loaded tuning fork
26.8.3 Superposition of waves of
equal frequencies with tuning forks
26.3.3.5 Tuning forks automatically move ping-pong
balls
26.6.20 Tuning forks on resonance
boxes
26.3.3.4 Sound wave patterns of a tuning fork,
waveform of a tuning fork
26.5.2 Speed of sound with a tuning
fork
26.3.1.2 String resonates with tuning fork
26.3.1.6 Velocity of sound in air and frequency
of a tuning fork
26.3.1.6 Velocity of sound in air and frequency
of a tuning fork
4.94 Wave patterns of a tuning fork
26.1.0 Wave properties of sound, sound waves, vibrations,
oscillations
26.1.0 Wave properties of sound, sound waves
26.1.14 Feel vibrations with a balloon
26.1.4 Oscillation of grains
26.1.2 Oscillation of object and production of
sound
26.1.3 Oscillation of ruler, vibrating rulers
26.1.7 Oscillation of soap film
26.1.6 Oscillation of tuning fork in water
26.1.5 Oscillation of your throat
26.1.16 Paper over vibrating string
26.3.2.8 Reed vibrations
26.1.9 Vibrating drums and balloons, ping-pong
ball and tuning fork
4.95 Seeing and feeling vibrations
that make sound waves
4.93 Sound waves patterns
26.4.1 Sound waves cannot travel
through a vacuum
26.1.1 Sound wave patterns, oscillations, origin
of sound, tuning fork vibration
4.98 Sound waves travel through
wood
4.97 Vibrating cans, string telephone
26.1.11 Vibrating cans
26.1.13 Vibrating desk, blackboard, chalkboard
26.1.15 Vibrations in a bowl
26.1.0 Wave properties of sound
Sound and vibration, oscillation, longitudinal and transverse waves,
standing waves, nature of sound, medium, vibrating objects, compression
and rarefaction, sound wave patterns, frequency and wavelength, audible
limits, infrasound, ultrasound, ultrasonics
See diagram 25.2.2:
Particles in a longitudinal wave
1. Sound wave is the mechanical wave motion when sound energy travels
through a medium. Sound waves are compression waves in a material medium
such as air, water, or steel. When the compressions and rarefactions of the
waves strike the eardrum, they result in the sensation of sound, provided
the frequency of the waves is between about 20 Hz and 20 000 Hz. Waves with
frequencies above 20 kHz are called ultrasonic waves. Those with frequencies
below 20 Hz are called infrasonic waves. The word "sound" refers to the
sensation when the eardrum reaction to vibrations. Sound waves require vibration
of the molecules or particles of their medium. Sound is a longitudinal wave
motion and will not pass through an evacuated space.
2. A vibrating source of sound produces a series of alternate compressions
and rarefactions that can travel as a longitudinal wave through a medium,
e.g. air, water, wood, but not through a vacuum. The particles of the
medium vibrate forwards and backwards in the same directions as the wave
is travelling. For example, a loudspeaker cone vibrates forwards to produce
a compression, "thicker air", and backwards to produce a rarefaction,
"thinner air".
3. Sound waves can:
3.1 reflect, e.g. echoes,
3.2 refract, i.e. bend towards the normal when pass into media in which
their speed is slower,
3.3 diffract, e.g. you can hear people talking around the corner or
on opposite sides of a large tree trunk,
3.4. form interference patterns, e.g. beats.
4. Sound travels as a wave in which motion the movement of the particles
is transmitted but not the physical particles themselves. In a transverse
wave the particles oscillate perpendicular to the direction of the wave.
Sound waves are longitudinal waves so the particles oscillate parallel
to the wave's direction of wave travel. Sound waves have a length, amplitude
and frequency.
5. Wavelength is the distance from one part of one wave to the same
place on the next wave, e.g. the distance from the place of maximum compression
to the next place of maximum compression.
6. Amplitude is the difference between the pressure in the compression
or the minimum pressure in the rarefaction and the pressure of the normal
undisturbed air.
7. Frequency refers to how often a rarefaction/compression pair pass
a given point in a second, e.g. a tuning fork for the A above middle C
vibrates 440 times every second or at 440 Hz. Frequency, f, is the number
of compressions per second. The distance between compressions is the wavelength.
Speed = frequency × wavelength.
8. The speed of sound is faster in solids than liquids gases, e.g.
The speed of sound in air at 0oC = 331 ms -1, dry
air 331.4 ms-1, fresh water 1 410 ms-1, sea water
1 540 ms-1, wood 3 850 ms-1, and steel 6 000 ms-1
at 0oC, Speed of sound is independent of pressure but is
proportional to the square root of the absolute temperature, so speed of sound
increases at higher temperatures. Since all sounds travel at the same speed
in the same medium, the higher the frequency the shorter the wavelength. Wavelength
or frequency determines the pitch of the sound. Amplitude determines its
loudness. The speed of sound also increases with the intensity of the source.
e.g. explosions.
9. Ultrasonics, supersonics, are vibrations whose frequencies are higher
than the upper audibility limit for humans, i.e. 20 kHz. Sound waves
show reflection, e.g. echoes, and refraction, bend towards the normal
when pass into media in which their speed is slower, e.g. you can hear
people talking around the corner or on opposite sides of a large tree
trunk. Ultrasonic waves are used by bats for navigation in the dark. and
used by ships in the ultrasonic system called sonar to find fish and measure
the depth of the sea. For jet planes the speed of sound is measured in Mach
numbers (Ernst Mach 1838-1916). A Mach number is the ratio of the velocity
of an object in air to the velocity of sound in air. Sonic speed = the speed
of sound. Subsonic speed < speed of sound. A jet plane travelling at supersonic
speed, i.e. > Mach 1, is travelling faster than the speed of sound and
leaves a cone shaped shock wave behind it heard as a very loud noise called
a sonic boom. A jet plane "breaks the sound barrier" when its speed increases
through Mach 1. The sound barrier divides subsonic speed from supersonic
speed. The first pilot to "break" the sound barrier and survive was Captain
Chuck Yeager in 1947 working in an US government program.
26.1.01 Beats with two tuning forks
See diagram 26.1.01: Beats with two tuning
forks
Superposition of sound waves of similar frequency produces pulsation
called beats that consist of booming sounds of wave reinforcements alternating
with quieter sounds of wave annulments. The number of beats per second depends
on the difference between the frequencies, e.g. 2 beats per second will
occur with combined frequencies of 200 Hz and 198 Hz.
Use two identical tuning forks. Load one of the tuning forks with a
piece of adhesive tape to change its natural frequency of vibration. Strike
both tuning forks and hear the "beats".
26.1.1 Sound wave patterns, oscillations, origin
of sound, tuning fork vibration
See diagram 26.190: Sea waves and sound waves
The number of complete vibrations in one second is the frequency of
a particular vibration. The way in which different sound frequencies combine
is analogous to water waves. Ocean waves are longest, i.e. of low frequency.
Let a small motorboat pass over these waves. The boat sends out its own
waves, which have a higher frequency than ocean waves. Wind will make
tiny ripples across the surface of the motorboat waves. The ripples usually
have an even higher frequency than the other two. Now these three vibrations
combine to form a pattern.
26.1.2 Oscillation of object and production of sound
Fasten one end of an elastic or other elastic tape to a nail on a wall
or the handle of a door. Strain another end of the elastic with your hand
and pluck the tightened elastic with a pencil. Observe its oscillation
and listen to its sound. Repeat the experiment but suddenly hold the oscillating
elastic with your hand when hear the sound of the elastic. The sound will
disappear immediately.
26.1.3 Oscillation of ruler, vibrating rulers
See diagram 26.1.3: Vibrating ruler
1. Place a ruler, or a steel saw blade, flat on the edge of a table
and the ruler extends about 15 cm out of the edge vertically to the edge.
Press the end of the ruler on the table with your hand; press another one
with another hand then suddenly leave your hand off it. Observe its oscillation
and listen to its sound. Repeat the experiment but suddenly hold the oscillating
end of the ruler with your hand when hear its sound. The sound will disappear
immediately.
2. Use rulers of different length, material and thickness. Hold a ruler
firmly to the edge of a desk with one end overhanging. Flick the free end
of the ruler and listen to the pitch. Change the length of the overhang
and again flick the ruler. Hold two rulers of different thickness or materials
so that they both overhang the same distance. Note how do their pitches
compare.
26.1.4 Oscillation of grains
1. Place several grains of rice on a drum surface or upturned loudspeaker.
Give the drum a beat. Listen to the sound of the drum and observe the
movement of the rice at the same time. If no drum, place the sound box
of a recording machine or acoustics level on a table, its right side up,
instead of a drum. Place several small pieces of paper on the cloth of the
sound box. Choose a piece of music with more bass and turn up the volume.
Observe that the paper oscillates along with the music.
2. Make some different sized drums by stretching tracing paper tightly
across the mouths of the jars. Fix the paper in place using rubber bands
or a pieces of string. Tap the paper lightly with a pencil to make a sound.
Can you see the paper vibrate? Now place some rice or other small grains
on the paper and tap it again. What happens to the grains? How does the
size of the drum affect the sound made and the behaviour of the grains? Make
some different sized drums by stretching tracing paper tightly across the
mouths of the jars. Fix the paper in place using rubber bands or a pieces
of string. Tap the paper lightly with a pencil to make a sound. Can you see
the paper vibrate? Now place some rice or other small grains on the paper
and tap it again. What happens to the grains? How does the size of the drum
affect the sound made and the behaviour of the grains?
26.1.5 Oscillation of your throat
Place your finger on your throat then speak. Feel and experience that
the throat oscillates when it speaks. Try to stop pronouncing suddenly during
speaking. experience that the oscillation of the throat will stop suddenly
too.
26.1.6 Oscillation of tuning fork in water
Hang a tuning fork with a thread. Strike it to start its oscillation.
Then quickly let its lower end touch the surface of water at a basin. Observe
the phenomenon appearing on the water surface when the sound of the tuning
fork starts. Touch the tuning fork with your hand and observe the disappearance
of the sound and the change on the water surface. Dip your finger rhythmically
into water and see the pattern of concentric vibrations.
26.1.7 Oscillation of soap film
Make a soap film on a brass wire ring. Hold it until the unwanted water
drops away completely. Look for the angle at which you can best observe
the soap film. Put the soap film at the place where it can be watched clearly
and is closest to your mouth. Constantly speak monosyllabic words loudly.
Observe the oscillation of the soap film. You can see similar oscillations
of window glass when a big truck passes.
26.1.9 Vibrating drums and balloons, ping-pong ball
and tuning fork
1. Tape the string to the ping-pong ball and hang it touching one side
of the drum. Gently hit the other side of the drum and measure how far the
ping-pong ball bounces off the side of the drum. Repeat the experiment by
hitting the drum harder.
2. Tape the string to the ping-pong ball and suspend it in a clear
space. Tap the tuning fork to set it vibrating and place it next to the
ping-pong ball and observe its movement.
3. Touch the end of the tuning fork on the surface of a bowl of water.
Observe the movements in the water.
4. Inflate a balloon. Use the first finger and thumb of both hands
to pull out the neck to make a slit and let the air out of the balloon.
Observe the vibrations in the neck of the balloon.
5. Place an empty coffee tin on the palm of your hand. Shout into its
open top and feel the vibrations on your hand.
5. Make some different sized drums by stretching waxed paper tightly
across the mouths of jars or other containers. Fix the paper in place with
rubber bands or string. Tap the paper lightly with a pencil to make a sound.
Observe vibrations in the waxed paper.
Place rice grains on the paper and tap it again. Observe the movement
of the rice grains. Note whether the size of the drum affects the sound
made and the behaviour of the grains.
When you tap the drum or the tuning fork it vibrates As the vibrating
surface moves in one direction it pushes molecules of air away from itself.
As it moves back in the other direction, pushing the molecules on its other
side in the opposite direction, it leaves a "gap" on the first side. In
a sphere around the vibrating object, the molecules of air am alternately
compressed and decompressed. This produces compression and rarefactions
in the air. These compressions and rarefactions are longitudinal compression
waves and produce sound. Loudness or volume is determined by the distance
of the sound source from the ear, the duration of the sound and the intensity
of the energy transmitted per unit area per unit of time.
26.1.10 Vibrations that make sound waves
See diagram 26.194: Make string sounds | See diagram 26.1.3: Vibrating ruler
1. Stretch and pluck rubber bands and the strings of string instruments.
2. Hold a ruler on the edge of a desk with 15 cm extending over the
edge and pluck it.
3. Put a drum on a desk and scatter puffed cereal grains or pieces
of tissue paper or cork across the top. Strike the drum and watch the vibration.
4. Press the thumb and forefinger against the larynx and make a low-pitched
sound with the voice. Feel the own sound vibration.
5. Hold a tuning fork loosely by the handle and strike the prongs against
the edge of the desk. Note what you hear. Again, strike the prongs and
quickly touch water in a pan with the tips of the prongs. The vibrating
fork splatters the water.
6. Stretch and pluck rubber bands and available string instruments.
Hold a ruler on the edge of a desk with 15 cm extending over the edge and
pluck it. Put a drum on a desk and scatter puffed cereal grains across
the top. Strike the drum and watch the cereal grains vibrate. Press your
thumb and forefinger against your larynx and make a low pitched sound with
your voice. Feel your own sound vibration. Hold a tuning fork loosely by
the handle and strike the prongs against the edge of the desk. What do
you hear? Strike the prongs again, and this time quickly touch water in
a pan with the tips of the prongs. What happens? The vibrating fork splatters
the water.
26.1.11 Vibrating cans
Punch a small hole in the bottom of a used metal can. Put a stout string
or a fishing line through it with its end tied tightly to a pencil inside
the can. Rub resin on the string. Hold the can with one hand and keep
the string taut with two fingers. Now draw your fingers along the line.
Sound comes from the can. Repeat the experiment of drawing your fingers
along the line at different speeds. Note the different pitches of sound.
26.1.13 Vibrating desk, vibrating blackboard, chalkboard
Tap a pencil on the edge of a desk at different points along its length
while pressing your ear to the desk Strike a tuning fork on a hard surface
and hold its stem firmly on the blackboard. The blackboard will sing to
the students!
26.1.14 Feel vibrations with
a balloon
Hold a blown up balloon between your hands at a short distance from
a radio speaker. Feel the vibrations in the balloon.
26.1.15 Vibrations in a bowl
Fill a glass bowl to such a depth that when you rub the rim of the
bowl with your wet fingers clear note is produced. Lower a lead sinker
or ball bearing suspended by fine thread until the side of the bowl is
.touched. The heavy object is flung violently outward. Repeat the experiment
by lowering the heavy object to touch a vibrating tuning fork.
26.1.16 Paper over vibrating
string.
Drop a v-shaped piece of paper over the vibrating string of a stringed
instrument, e.g. a violin string, and observed the resulting motion.
26.2.0 Pitch, frequency
Octave, quality (timbre) loudness, audibility, decibel (dB), sound
intensity, Doppler effect, noise, harmonic, siren, sound pressure level
1. The sounds you hear are the result of perceiving by your ear the
oscillations of an elastic medium, usually air. Sound can be described
both in terms of its physical nature and your psychological reaction to
it. As a physical wave, a sinusoidal sound wave has a frequency. your psychological
reaction most closely related to frequency is pitch, i.e. the highness
or lowness, or "bass" or "treble" of your reaction. The range of frequencies
to which your ears are sensitive is about 20 Hz to 15 000 Hz. Frequency
is the primary stimulus for pitch although many people hear a small pitch
change when the intensity of a constant frequency sound is changed. Pitch
refers to when you hear different frequencies of vibration that are called
differences in pitch, i.e. higher frequencies as high notes and lower frequencies
as low notes. When you think of a sound (say, a musical note) as either "high"
or "low", you are referring to its pitch. The higher, the higher the pitch
of the sound. When you think of a musical note as either "high" or "low",
you are referring to its pitch. The higher he note, the higher the pitch
of the sound. Sounds with the same pitch, e.g. musical note, produced by
different sources, e.g. piano, flute, violin, sound different due to the
quality, or timbre, of the sound causes by extra small waves called harmonics
that add quieter sounds to the main sound of the instrument.
2. Intensity is a physical parameter associated
with sound related to the sound energy crossing a region in space per unit
area per unit time. The intensity, I, of a wave is the energy per unit
area, per unit time. In practice, it is the average power carried by the
wave through a unit area perpendicular to the direction of propagation of
the wave. If at time dt an amount of energy dE is carried through an area
dA perpendicular to the propagation direction of the wave. Then I = dE /
dA × dt = Power per unit area, W /m2.
3. The psychological reaction to intensity is loudness.
If the intensity of a sound is increased, the sound is perceived as louder.
Loudness, however, is strongly dependent on frequency. If the physical
intensity of a sound is kept constant and the frequency is changed, the
resulting psychological loudness varies significantly. Loudness increases
as the size (or amplitude) of the sound vibrations increase. Loudness (or
sound pressure) is measured in decibels (dB). 30 dB has ten times more intensity
than 20 dB. 40 dB has tens times more intensity than 30 dB. In other words
40 db has 100 times more intensity than 20 dB. Sounds consistently greater
than 80 dB will damage your heating, however, home fire alarms may emit beeps
of 85 dB when being tested and when the alarm sounds. Sounds greater than
140 dB may burst your eardrums. As sound travels from its source the amplitude
decreases so the loudness decreases.
4. As you play a cassette place your hand against
the speakers. Feel the vibrations as you turn up the volume. Investigate
production of bass sounds on modem high fidelity speakers. Feel the air
puffed out at high volumes.
5. Some sound levels (dB): Threshold of hearing
0, Rustle of leaves 10, Whisper (at 1 m) 20, City street, no traffic 30,
Office, classroom 50, Normal conversation (at 1 m) 60, Jackhammer (at 1
m) 90, Rock band 110, Threshold of pain 120, Jet engine (at 50 m) 130, Saturn
rocket (at 50 m) 200.
6. The power of sound is very low. An orchestra
of 75 persons playing at its loudest only produces about 70 watts of acoustic
sound power. The human car can detect tones with a power output of a
millionth of a watt per square metre of area in those frequencies to
which it is most sensitive. Snow absorbs most of the sound energy that hits
it. However, it makes no difference how loud or long you shout at it, you
will still not produce enough energy to melt the snow. A crowd of 80 000
people at a football stadium makes a lot of noise, but they do not generate
enough energy over a 90 minute match to cook an egg. As sound waves move
away from their source their intensity decreases rapidly according to the
inverse square law. Sound travels further over water. This may happen if
there is a warm layer of air over the water. When the sound hits this layer
it will travel faster and therefore further.
7. Concert pitch is the degree of sharpness of flatness
used by a group of musicians playing in concert. The most common value
of concert pitch is that the A above middle C should be be tuned to 440 Hz,
but higher concert pitches are becoming popular. Before a concert starts,
the separate members of the orchestra tune their instruments to a note
given out by the principal oboe, although this could be done by using a well
tuned piano.
26.2.1 Pitch and length
See diagram 26.2.1: Pencils between string
and meter stick | See diagram 26.2.1.2: Finger
on string
1. Tie a loop of string to just fit tightly around the length of a
metre stick. Insert two pencils between the string and the metre stick
at each end. Insert two pencils at each end between the string and the
metre stick. Pluck the string in the centre and note the pitch and loudness.
Put the metre stick on the desk to amplify the sound.
2. With one finger push the string down on the metre stick at the centre
and use another finger to pluck gently the string on one side. Note how
the pitch and loudness changes. Move your finger to different positions
along the metre stick and pluck on either side. Note how changing the length
of the plucked string changes the pitch.
3. Tie a loop of string to just fit tightly around the length of a
metre stick. Insert two pencils between the string and the metre stick
at each end. Adjust the tightness of the string by pushing a ball point
pen cap between one end of the string and the metre stick. Place the metre
stick flat on a table. Pluck the middle of the string. Note the pitch and
loudness. Move the ball point pen cap to different positions to lengthen
or shorten the length of string that can be plucked. Note the relationship
between length of string plucked and pitch. Compare the pitches of the two
sides of the string and observe the relationship of the pitches to the lengths
of two sides of the string.
4. A similar experiment uses an empty box or container with one small
side cut out and a rubber band stretched around.
26.2.2 Pitch and tension
See diagram 26.2.2
Use a ruler, fine string or fishing line, 2 ball point pens, tape.
Take the ball point pen inner out of one ball point pen. Tape the ball
point pens to each end of the ruler. Tie the string lengthways around the
ruler. Twist the ball point pen inner around the string on the under side
of the ruler. Make sure you use the empty end of the ball point pen inner.
Tighten the string by turning the ball point pen inner through half a turn,
and plucking the string each time. Stand the ruler on the desk. Note how
increasing the tension on the string changes the pitch. This can be shown
on a guitar and other stringed instruments. A similar experiment uses a bucket
half full of sand suspended by string. Keep adding sand and plucking the
string. Listen to the change in pitch.
26.2.3 Whirling pipes, pitch and length
Use 1 to 2 metre length of articulated vacuum cleaner hose or swimming
pool or bilge drain hose and string. Attach a string to one end, hold the
pipe in one hand and twirl it rapidly around. Note how the pitch changes
when you twirl it faster or slower. Note how different length pipes affect
the pitch. Note how the air flows down the tube when you twirl it. Australian
aboriginal people have such an instrument that Europeans call a "bull roarer".
26.2.4 Doppler effect, change in pitch
The Doppler effect is caused by the change in pitch due to relative
motion between sound source and listener. A listener approaching a stationary
sources of sound will hear a higher pitched sound. A listener moving away
from a stationary sources of sound will hear a lower pitched sound. You
can hear the effect when a train rushes past while sounding its horn or
whistle, or a car rushes past with the horn sounding or a police car rushes
past with siren sounding. If a moving source of sound emits a sound of
frequency fs, v = speed of sound, and the source of sound approaches the
observer at speed vs, measured relative to the medium conducting the sound,
an observer moving towards the source at speed vo will hear a sound of frequency
fo = fs(v + vo/ v - vs). When the source and the observer approach each
other, more wave crests strike the observer per second than when the source
and the observer are at rest, causing the ear to perceive a higher frequency
than the frequency emitted by the source. When the source and the observer
move away from each other, less wave crests strike the observer per second
than when the source and the observer are at rest causing, the ear to perceive
a lower frequency than the frequency emitted by the source.
See diagram 26.2.4: Swinging hand-held speaker
Show how the frequency of a moving sound source changes because of
the relative velocity of the source to the observer. For a sound source,
use a battery-operated oscillator driving a loudspeaker at constant frequency
f. Attach the sound source to a strong string. Hang on to the end of the
string then swing the sound source around and above head. The pitch of sound
from the sound source is heard to raise and lower as the the sound source
moves towards or away from the observer. If the length of the string = 60
cm, rotational frequency = 4 revolutions / second, linear speed = 15 meters
/ second, so maximum doppler frequency 1.04 f = and minimum doppler frequency
= 0.96 f.
26.2.5 Hanging buckets, change in pitch
See diagram 26.2.8
Use separate strings with different lengths to hang identical buckets
full of sand. Strike each string and note the pitch. Note that strings under
the same tension, the pitch are depends on the length. The longer the string,
the lower the pitch. Players of stringed instruments apply this principle
to change the length of the string to control the pitch of a musical instrument.
26.2.6 Thin and thick strings, change in pitch
See diagram 26.2.9
Repeat experiment 26.2.1 but with two strings, one thick and one thin.
To make the tensions as equal as possible add a spacer on the underneath
for the slacker string or hang a bucket of sand of the same mass. from each
string. Note how increasing mass of the band change the pitch.
26.2.7 Stretched rubber band,
change in pitch
Hold a thick rubber band slightly stretched between your thumb and
first finger. Pluck it with the first finger of your other hand while
holding it near your ear. Note the pitch of the sound. Keep plucking it
while stretching it more. You expect the pitch to become higher as you
stretch the rubber band but it may seem to have the same pitch while you
stretch it or even to have a lower pitch! When you tighten the string
of a sonometer or a violin the string emits a higher note because the tension
in the string has increased. Also, the length and density of the string has
hardly changed. However, when you tighten an elastic band over your finger
and thumb the tension, length and density change enough for their effects
to compensate each other. If you stretch three identical rubber bands over
an empty match box and increase the tension of two of the rubber bands with
match sticks between the rubber bands and the side of the match box, the
pitch does increase with tension. The lengths of the rubber bands stretched
over the ends of the empty match box have much the same density and length
but different tensions.
26.2.8 Squealing balloon
Blow up a balloon. Pinch the neck with both first finger and thumb,
then pull apart while letting air escape from the balloon. The balloon
makes a high-pitched squealing noise with changes in pitch as you pull and
release the neck of the balloon. The escaping air molecules cause the
rubber in the neck of the balloon to vibrate to make the squealing noise.
26.2.9 Record player, change
in pitch
Use a record player with variable speed, 33 revolutions per minute
(33 rpm), 45 rpm, 78 rpm. If the 45 rpm record is played at 78 rpm, the
pitch is too high. If played at 33 rpm the pitch is too low.
26.3.0.0 Resonance, standing
waves (stationary waves)
See:
Standing waves, School of Physics, University of New South Wales. [Animations
needs Flash 8 Plugin.]
See diagram 26.3.0: Standing waves in a string
| See diagram 26.3.01: Standing waves in air
columns
Resonance is the phenomenon of rapid and uncontrolled increase in the
size of a vibration when the vibrating object is subject to a force varying
its natural frequency. An object which can vibrate has a natural frequency
at which it will do so. An object may be forced to vibrate at a variety
of frequencies. As recorded in the Bible, Joshua built the Walls of Jericho
for protection from his enemies. They were solidly built but they did not
do him any good when they came tumbling down at the blast from a troop of
trumpeters. What do trumpets and the Walls of Jericho; opera singers and
glasses; and soldiers marching on bridges have in common? All bodies vibrate
at their normal frequency. Resonance occurs when the frequency of a sound
source coincides with the natural frequency of the body.
A string will resonate only if a whole number of segments, each ½
× wavelength long, exactly fit on the string. Length of resonating
string = n (½ wavelength) where n is any integer. The fixed ends
of the string must be nodes. wavelength = vT = v / f so during resonance
the shorter the segments the higher the resonance frequency.
Longitudinal waves, compression waves occur as length wise vibrations
of air columns, liquid volumes and solid bars. At resonance, nodes exist
at fixed points, such as the closed end of an air column in a tube, or the
location of a clamp. A diagram such as 26.3.0 can be used to show the resonance
of longitudinal waves as well as transverse waves. The diagrams specifically
for longitudinal waves are used just to indicate the locations of nodes
and antinodes, the distance between node and adjacent antinode is 1/ 4
wavelength.
The player of an oboe blows air in between two reeds joined together
as a mouthpiece so that they vibrate against each other to produce a standing
wave in the main body of the instrument.
26.3.0.1 Wine glass resonance
See diagram 26.3.0.1: Singing glass | See diagram 26.3.0.2: Wine glass resonance
1. Use a good quality wine glass. Hold firmly the base of a wine glass
to the table with one hand. Wet a finger on the other hand then slowly wipe
around the rim of the wine glass. Gradually change the speed of rotation
until a continuous ringing sound is heard. Observe the vibration on the
surface of the water. Feel your finger gripping the rim of the glass as
you rotate you finger. Note what you feel when you reach the resonant frequency
of the glass.
2. Use two similar thin walled glasses, e.g. wine glasses, on a table
2 cm apart. Rub your clean finger around the rim of one glass until you
hear a humming ("whining") sound. The second glass will also start to vibrate
and produce a sound. To see the second glass vibrating place a very thin
wire across the rim of the second glass or put the same amount of water
in both glasses and observe the surface of the water in each glass. The
second glass resonates with the first glass. The pitch, note, produced
by the two glasses are the same.
3. Clean your hands and place two clean wine glasses on a table. Hold
one wine glass tightly with a hand and make it touch the tabletop tightly.
Put a drop of vinegar on the index finger or thumb of another hand then
rub the wine glass very slowly with the finger. You can hear the sound from
the wine glass. Pour water into the wine glass then rub it again. The pitch
of the sound will change. The finger is the vibrating source as it jolts
over the surface of the glass due to friction. If your finger is greasy it
just slides over the glass and no sound is produced. The wine glass is like
a resonance box. Rubbing causes the resonance. Thus the pitch of the sound
depends on the wine glass. If you pour water into the wine glass, the mass
increases and the pitch of the sound produced decreases. Soldiers marching
across a bridge in step can cause the bridge to vibrate violently if the
frequency of their steps coincided with its natural frequency. So when approaching
a bridge the officer in charge should order "Break step!" so that the soldiers
do not keep in step and cause a dangerous vibration.
4. Position a clean wine glass near a horn loudspeaker. A light mirror
acts as a detector of resonance. Adjust the frequency of the signal generator
through the 1000 to 1600 range until a circular Lissajous figure projected
on the screen indicates resonance. Increase the amplifier output until
the wine glass explodes because of the rim oscillations.
26.3.0.2 Insect footsteps in a paper bag
Trap a housefly in a smooth paper bag, seal it, and hold it horizontally
above your car. If you are in a quiet room you can hear the patter of
the six legs and other rather curious noises quite clearly. The paper
behaves like the skin of a drum. Although only the tiny legs of the insect
beat on it, it begins to vibrate and transmits such a loud noise that you
might imagine a much larger animal was in the bag.
26.3.0.3 Spray from "fish wash" dishes in Chinese
temples "frictionizing" the brim, stationary waves
The "fish wash" can still be seen in ancient Chinese temples. It is
a basin made of brass with two circular holders on each side of it, called
"wash ears". The name "fish wash" came from the picture of fish at the bottom
of the "wash". The fish wash can be used for an example of the phenomenon
of resonance. Fill the fish wash with water, wash your hands clean, then
rub with two hands on the top of the "wash ears". When your hands rub synchronous
back and forth on the wash ears, the fish wash can buzz loudly and form
sprays. If you can rub continuously enough, the spray jump very high as
if to spout though from the mouth of the fish. As you rub the wash ears with
your hands, the fish wash can produce vibration with the frequency of rubbing.
When the frequency of vibration caused by rubbing is equal to or near to
the natural frequency of the vibrating object, the brass wall of the fish
wash produces resonance, the amplitude increases rapidly. However, due to
the limitation of the bottom of fish wash, the vibration produced by it can
be spread out. Then the incident wave and reflected wave pile up each other
at the wall of the fish wash to form a stationary wave. The point of maximum
amplitude is at an antinode, the point of minimum of amplitude is at a node.
It is easiest to produce a low resonance frequency by rubbing an object
like a circular basin, i e. a vibration consisting of four antinodes and
four nodes. The place at maximum amplitude is on the wall of the wash can
stimulate the surface of water immediately to form the spray. As the four
antinodes act in the meantime, there appears the spray splashing in all
directions. If you paint four fish at the places where the amplitudes are
maximum on the wall of the fish wash, the spray comes as though from the
mouths of the fish.
26.3.0.4 Amplify sound from a comb, comb resonator,
chimes
See diagram 26.3.0.4
1. Hold a wooden comb in the air and strike the teeth of the comb with
your nail. Ask another student to listen to the sound at a certain distance
from you. This student hears the reference sound and must compare this
sound to all the following sounds
2. Repeat the experiment by holding the comb firmly and vertically
on a wooden table. Striking the comb with the same force as before. The
surface are of the vibrating object, i.e. comb and table top, has increased
so sound is louder.
3. Repeat the experiment but strike the comb with a stronger force.
The larger the magnitude of the force striking the comb, the larger the
amplitude of the vibration of the sound source, viz. the larger the energy
of the sound source, the large the amplitude of the vibration received,
the louder it sounds. The amplitude of vibration of the comb teeth has
increased so the sound is louder
4. Repeat the experiment with a plastic comb. Compare the sounds.
5. Repeat the experiment at different distances from the hearer. For
the same sound source, the farther the sources the lower the sound heard
because the less the energy distributed to the ear the lower the intensity
of the sound.
6. Repeat the experiment with the comb held against a small wooden
box. A wooden box is best for making a sound amplifier because it has
the best resonance effect. So the bodies of guitar and violin and the
sound box of loudspeaker are made up of wooden material.
26.3.0.5 Drink-can to amplify the sound of a thread
Use a 1 m long, thick, silk thread or fishing line. Rub the thread
with a block of rosin. Lift one end of the thread and let it fall free.
Listen to the sound of the thread. Use an empty drink-can. Punch a hole,
slightly thicker than the thread, on the bottom of the can. Insert one
end of the thread into the hole and tie the end to a short pencil. Lift
another end again and let the can fall free. Note the sound of the can.
Rub the thread down with your hand. Note the sound from the can.
26.3.0.6 Tap different containers
Listen to the sound each makes. Can you hear any differences? Sort
the containers by quality of sound. Listen for a good ringing sound and
a flat sound. Next examine the containers in each group. Which group contains
the cracked containers? Railway workers used to tap train wheels to find
if they had developed faults. The faulty wheels sounded different. Tap each
container in turn. Listen to the sound each makes. Can you hear any differences?
Sort the containers by quality of sound. Listen for a good ringing sound
and a flat sound. Next examine the containers in each group. Which group
contains the cracked containers?
26.3.0.7 Cellophane noise
Use a piece of cellophane 5 cm square. Stretch it tightly between the
thumbs and index fingers of both hands. Hold your hands in front of your
face so the cellophane is in front of your lips. Blow hard and fast at the
edge of the tightly stretched piece of cellophane. Keep your lips close together.
You must send a thin stream of air right at the edge of the cellophane.
Can you hear a noise? When the air hits the edge of the cellophane, you
will make a scream. If you don not change the distance between the cellophane
and your lips until the air hits it just right. The fast moving air from
your lip makes the edges of the cellophane vibrate. Because the cellophane
is very thin, the jet of air makes these vibrations very fast The faster something
vibrates the higher the tone it creates.
26.3.0.8 Knocking sounds
Place an empty beaker on several pieces of paper. Knock the beaker
side gently with a glass stick to emit a harmonic sound like "jow", the
sound of a bell. Place a china dish instead of the beaker on the paper
then knock it with the glass stick. It sounds very long and pleasant to
ear. Polish a flowerpot with a piece of sand paper. It emits very loud noise.
Many people try to cover their ears when they hear the sound that they do
not want to hear. Use two pieces of hard foams. Press them together then
rotate them at the opposite directions. It may emit noise too. Inflate then
puncture it with a nail. A shocking "bang" sounds suddenly.
26.3.0.9 Knocking on bottles,
blowing over bottles
See diagram 26.3.1.6: Bottle sounds
1. Use 3 identical empty bottles, 1/3, 1/2 and 2/3 filled with water.
Lift each bottle by the neck and strike with a stick. The bottle and water
vibrate so the more water in the bottles the lower the pitch. So the sound
from the 2/3 filled bottle has the lowest pitch.
2. Repeat the experiment by putting your lower lip on the mouth of
each bottle and blowing gently. The air above the water in the bottles
vibrates to make a sound. The larger the amount of air in the bottle the
lower the pitch. So the sound from the 1/3 filled bottle has the lowest
pitch.
3. Repeat the experiment by filling the bottles with equal volumes
of heavy oil or water or kerosene. Lift each bottle by the neck and strike
with a stick. The bottle and added liquid vibrate so the heavier the bottle
and contents the lower the pitch. So the sound from the bottle containing
oil has the lowest pitch.
4. Repeat the last experiment by putting your lower lip on the mouth
of each bottle and blowing gently. The air above the water in the bottles
vibrates to make a sound. The larger the amount of air in the bottle the
lower the pitch. All bottles contain the same volume of air so the sounds
from the three bottles have the same pitch.
26.3.0.10 Aeolian harp,
wind harp
Wooden resonating box with strings stretched across two sound bridges
and tuned to the same note or different notes. Sound is cause by vortexes
as air passes around the strings to vibrate them and to produce a chord.
An aeolian tone is a musical note caused by an air vortex action on a stretched
string in an air stream. The sound produced may rise and fall through a
harmonic series as the wind speed varies. The sound occurs around "singing"
power lines, car aerials and boat rigging during a gale.
26.3.1 Musical instruments, resonance in strings
Monochord, free and forced vibrations, sound from stringed instruments,
monochord, free and forced vibrations, standing waves, tones, sonometer,
vibrating strings, fundamental
The earliest stringed instrument was perhaps the Greek lyre, some being
strings stretched on the shell of a tortoise. Stringed instruments have
stretched strings that vibrate when plucked or when a horse hair bow slides
across them. The strings of a violin are stretched across a wooden bridge
that conducts vibrations into the sound box that in turns resonates to
give a louder sounds with different characteristics. Piano strings vibrate
when hit with hammers covered in felt controlled by the keys of the keyboard.
26.3.1.1 Paper rider thrown
off vibrating string
See diagram 26.1.12 | See diagram 26.2.1.2
1. Use a board; a pulley; some weights; two ball point pens; a tuning
fork; a piece of string. Fix one end of the string on the board and another
one is tightened by the weight through the pulley. Insert the two ball point
pens between the string and the board. Strike the tuning fork to start
its oscillation and let it touch the board. Does the string vibrate to sound?
Add the weight to adjust the tension of the string or remove the ball
point pens to change the length of the string so that the string vibrates
at the frequency of the tuning fork and its amplitude and loudness reaches
the maximum. That is the string resonates with the tuning fork and a standing
wave forms on the string when the frequency of the string matches the frequency
of the tuning fork.
2. Cut a cardboard into a paper horse. On the paper horse drill a hole
at some point, higher than its gravity centre. As before, make the string
resonate with the tuning fork and a standing wave forms on the string.
The paper will move when the resonance occurs. When a standing wave forms
on the two fixed ends of the string, the two ends must be nodes of the wave
and the antinode must be between the two ends. If the wave caused by the
tuning fork is fundamental, the amplitude of the paper horse may reach the
maximum.
26.3.1.2 String resonates with tuning fork
As in 26.3.1.1 make the string resonate with the tuning fork. Change
the position of the ball point pen a bit to change the fundamental of the
string slightly. Strike the tuning fork and the string at the same time
to make them sound. listen to the sounds. You may hear each vibration and
the slow and steady sound of "pat". Adjust the position of the ball point
pens so that the frequency of the "pat" sound is slower and slower and finally
disappears, when the string resonates with the tuning fork again. When
two vibrations with similar frequencies exist at the same time, not only
each of their sounds may be heard, but also they may be superposed to form
a slow and steady frequency, named "pat". The frequency of "pat" is the
distance of the two frequencies.
26.3.1.3 String vibrates at constant tension
If a string vibrates under constant tension, the frequency n is inversely
proportional to the length, L, i.e. n is proportional to 1/L.
1. Move bridge B so AB, L, = 80 cm. Adjust load, T, until note from
wire is same as note from tuning fork. 2. Keep tension of wire constant,
find lengths AB, i.e. L, that vibrate with the same frequency as tuning
forks with different frequencies, e.g. 256, 320, 384, 426, 512 cycles per
second, using paper rider method or beats method. Plot a graph of n, cycles
per second (y axis) against 1/L, cm (x axis). If points on the graph are
in a straight line passing through the origin, n is proportional to 1/L
26.3.1.4 String vibrates at constant length
If a string vibrates at constant length, the frequency n is directly
proportional to the square root of the tension T, i.e. n is proportional
to √T
Use a 1.5 kg load. Move bridge B to adjust the length AB, L, of the
vibrating string until it vibrates with the same frequency as the lowest
frequency tuning fork, using paper rider method or beats method. Record
the load, T, and the frequency of the tuning fork, c. Mark the position
of bridge B and do not change it. Use the tuning fork of the next highest
frequency and adjust the tension in the wire, T, until the frequency of
the sound from the wire is the same as the frequency of the tuning fork,
c. Repeat the experiment for all other tuning forks and record the values
of n and T. Plot a graph of n (y axis) against √T (X axis). If the points
on the graph are in a straight line passing through the origin, n is proportional
to √T.
26.3.1.4.1 Violin strings
and piano strings
A violinist draws the bow across the string at about 1 / 7 of the length
from the end to produce overtones and harmonics. Also the string can
be plucked there to produce pizzicato. The four strings produce the musical
notes E, A, D and G. The piano uses 88 keys to strike the 230 steel wire
strings under a tension of about 70 kg near the end.
26.3.1.5 Frequency of a tuning fork with a sonometer
See diagram 26.3.1.9: Sonometer, monochord
1. Find the frequency of a tuning fork with a set of tuning forks of
known frequencies. Adjust tension of wire, T, to same value. Find the length
AB, L, of the string under the same tension until note from wire is same
as note from the unknown tuning fork. From the graph locate L and the corresponding
value of the unknown frequency.
2. Find the frequency of a tuning fork using no other tuning forks.
Use a 2 kg load of say 2, 000 gm. Move bridge B to adjust the length AB,
L, of the vibrating string until it vibrates with the same frequency as
the unknown frequency tuning fork, using paper rider method or beats method.
If L > 25 cm increase load and repeat the experiment. Record length L
cm. of the vibrating wire, and load, T.
3. Cut length L from a reel of wire the same as used in the sonometer.
Find its weight, M. The frequency, n, of a length L cm of wire, of mass
per unit length M g / cm. under a tension T, = 1 / 2L √T / m cycles per second
26.3.1.6 Velocity of sound in air and frequency
of a tuning fork
See diagram 26.3.1.6
1. Find the velocity of sound in air at room temperature using the
closed resonance tube. The closed resonance tube AB is a tube of wide,
uniform bore, open to the atmosphere at A but closed by a water surface
at C. The length of the air column AC may be varied by moving the reservoir
R up or down or by moving AB up or down. Record the room temperature.
2. Sound the tuning fork of highest frequency just above A to increase
the length of the air column AC until the sound emitted by the vibrating
column of air is at maximum loudness. Now the fundamental frequency of the
air column is equal to the frequency of the tuning fork.
3. Record length L1 cm of the air column. Increase AC until you hear
a second point of resonance lower down the tube.
4. Keep the tuning fork vibrating and record the new length L2 cm of
the air column AC. Record the frequency n of the tuning fork used. When
resonance occurs at length AC = L1, then the column of air length (L1 +
e) cm = λ / 4, λ = wavelength of the tuning fork. The column of air that
vibrates is slightly longer than L1 and its extra length is called "e". When
resonance occurs at length AC = L1, then the column of air length (L1 + e)
cm = λ / 4, where λ = wavelength of the tuning fork. When resonance occurs
at length AC = L2, then the column of air length (L2 + e) cm = 3 ×
λ / 4.
L1 + e = λ / 4
L2 + e = 3 × λ / 4
(L1 + e = λ / 4L) - (L2 + e = 3 × λ / 4) = λ / 2
Velocity of sound = frequency × wavelength, v = n × λ,
v = 2 × frequency (L2 -L1) cm / second
5. Knowing the value of the velocity of sound in air, find the frequency
of the tuning fork.
26.3.1.8 Piano string resonance
Place a heavy object on the soft pedal of the piano to release the
dampers. Open the lid at the top of the piano and talk into the gap between
the strings and the back of the instrument. When you talk to the piano,
does it answer back? Play some different musical notes into the piano. How
does it respond to high notes and to low notes? Which parts of the piano
are responding to the sounds you are making? Investigate the strings in
the back of a piano or on a guitar. Note the changes in pitch that come
from different thickness, tension or length of the strings. Consider what
effect extended playing of a stringed instrument may have on pitch. Note
that as the instrument is played the temperature of the strings increase.
26.3.1.9 Monochord, sonometer,
string
See diagram 26.3.1.9 | See diagram 26.2.4
1. The first recorded monochord was invebnnted by Pythagoras, (570-500 BC),
who observed that the different musical notes from blacksmiths' striking
anvils with hammers depended on the weights of the hammers. So he invented
a monochord consisting of a stretched stringover a sounding boardwith one
end attached to a scale pan.The tension in the strung depended on the weights
in the scale pan. From these observations he devised the scale of eight notes,
the octave.
2. The monochord is a hollow wooden sounding box with a wire whose length
of vibration is adjusted by movable bridge B. Adjust the tension in the
wire with weights D. Pluck the wire between A and B at the centre so that
the wire between the bridges starts to vibrate and emits a musical note
of definite frequency. Change this frequency by changing the load so as
to change the tension in the wire or change this frequency by changing the
distance between bridges A and B. Use a tuning fork to "tune" the sonometer
to a sound of known frequency.
Verify Mersenne's laws, the equations for the vibration of a stretched
string.
For a string under constant tension the frequency varies inversely
as the length.
For a string of constant length the frequency is proportional to the
square root of the tension.
For a given length and constant tension the frequency varies inversely
as the square root of the mass / unit length.
3. Hear the same pitch: Sound the fork and wire alternately and adjust
the wire until you hear the two notes emitted to be equal in pitch.
4. Paper rider thrown off by resonance: Put a small piece of paper, "paper
rider", on the wire midway between the two bridges A and B. Strike the
tuning fork to set it vibrating and place the end of the handle firmly on
the hollow wooden box of the sonometer. If the fundamental note of the wire
has the same frequency as the tuning fork wire will start vibrating resonance
and the paper rider thrown off.
5. Listen to beats. When two notes of nearly equal frequency are sounded
simultaneously you hear a regular throbbing noise called beats. The frequency
of the beats is equal to the difference in frequencies of the two notes.
Sound the tuning fork and wire simultaneously and adjust the wire so that
the beats become slower then disappear because the wire and fork have the
same frequency. The fundamental note of the vibrating air column depends
upon its length so you can tune an air column to a tuning fork altering
its length
6. Oscillating frequency of a string is dependent on the tension acting
on the string and the length of the string. Prepare a strip of wooden board.
Nail two pieces of short boards on either end of the wooden board. Place
the board flat on a level tabletop, the two short boards below so that the
middle of the wooden board is in the air. Draw a straight line on the wooden
board. Screw three screws with the same sizes on the board. Prepare a piece
of long nylon string. Tie the string to the two screws at the two ends of
the wooden board. Adjust the direction of the groove on the top of the middle
screw so that the string goes through the groove. Screw the screws at the
two ends of the wooden board to tighten the string. Be careful not to make
the string too tight. Strike the string to make it emit a sound with a pitch.
Screw one of the screws at the two ends to make the string tighter. Strike
the string. Repeat the above steps several times and listen to the sounds
and compare the change in pitch. You may find that the tighter the string,
the higher its pitch, when its length does not change. Insert a small board
under the string so that the length of the string is changed. Also, place
a knife or a pencil under the string. They may separate the string to change
its length. Strike the string and compare the change in pitch of the string.
Repeat the above steps. Summarize the relationship of the length of the string
to the pitch. You may find that the shorter the string, the higher its pitch,
when its tension does not change.
7. Prepare an open mouth plastic box instead of the above wooden board.
8. Prepare a glass stick of 80 mm length. Insert it under the string. Strike
the string. The sound changes strongly obviously. Every stringed instrument,
such as a guitar and violin, has a gut made up of a wooden box. It may
enhance the sound and make the string sound partial tone that is producing
resonance. So the wooden box is also called a resonating box.
26.3.1.10 Pitch and mass
(density) of vibrating strings
See diagram 26.3.1.10
Pitch depends on the length, tension and thickness of the vibrating
string.
1. Use rubber bands of various sizes and masses, an empty box or container.
Pluck each band separately, and note their pitch. Cut out one large side
of the box or container. Stretch rubber bands of different sizes around
the box. Adjust the bands so that each has the same tension as near to
possible. Note how does increasing mass of the band change the pitch Strike
the strings one by one. Note their pitches. In addition using weights
hanged to do similar experiment. Use a wire and a rubber tape with the same
length.
2. Use two same kegs full of sand. Hang the two kegs with separate
wires and rubber tape. The wire and the rubber tape have the same inner
tension as they hang weights with the same weight. Strike the wire and
the rubber tape separately. Compare the difference in pitch. You may
find that they sound lower than the above experiment because the keg can
plays an important role of a resonance box besides as a backstop. Their
pitches are dependent on their mass or the density of the string, exactly.
The denser the string, the lower its pitch and vice versa.
26.3.1.11 Plastic bottle
guitar strings
See diagram: 26.3.1.11
Insert two nails side by side into one end of a piece of softwood timber
300 mm × 25 mm × 15 mm. Tie a length of fine wire to each
of the nails and hammer them into the timber. Screw two screw eyes side
by side into the other end of the timber. Cut rectangular holes in opposite
sides of the plastic bottle near its base so that you can push the timber
through the holes with the nails and wire are just poking through. Pull
the wires tight and tie the other ends to the screw eyes. Adjust the sound
of the strings by screwing the screw eyes to tighten the wires. Insert a
small wooden bridge between the wires and the base of the plastic bottle
26.3.2.0 Musical instruments, resonance in air
columns
S01
Singing rods, resonance in open rod, (commercial website) | S04 Sound tube,
Resonance from twirling (commercial website)
| Sound tube
(commercial website)
Sound from wind instruments, organ pipes, standing waves,
end correction, pitch and length, reed pipe, paper pipe, whirling pipes.
A sound synthesizer stores sound waves electronically as a binary code
that can later be converted to a variable electric current that controls
a loudspeaker.
26.3.2.1 Wind instruments
See diagram 26.3.2.1: Standing waves in
a flute
Wind instruments, e.g. pipe organs, flutes, oboes, clarinets, produce
their musical sounds by resonating standing waves in air columns. The air
columns are in tubes either open at both ends or closed at one end. In a
trumpet the player's lips vibrate in a cup-shaped mouthpiece but in a clarinet
or oboe air is blown between pieces of reed to cause them to vibrate. Standing
(stationary) waves can occur in air columns where tube is closed at one
end, e.g. flute, pan pipes, or in air columns where tube is open at both
ends, e.g. open organ pipes, saxophone, trumpet. In a flute or recorder
the player covers or uncovers holes to change the length of the vibrating
air column.
Nodes refer to longitudinal standing (stationary) waves in air columns
that always have a node at a closed end and an antinode at an open end.
Antinodes formed by standing waves in air columns at the open ends of any
tube are in located a small distance beyond any open end, called the end
correction. As the instrument is played, the air in the resonating column
becomes wanner and moister. Consider the effect of extended playing of
a reed instrument such as a saxophone or oboe will have on pitch. How might
these changes affect the total sound that an orchestra produces? How would
musicians avoid these problems?
26.3.2.2 Octave and pitch,
sol-fa (solfege) syllables
The interval between two musical notes that have fundamental frequencies
in ratio 2:1. Pitch refers to the sound you hear being high, high frequency,
or low, low frequency. Pitch is not quite the same a frequency because
at very high or very low frequencies the loudness affects pitch of the sound
you hear. An octave may be sung using the tonic (keynote) sol-fa (solfege)
syllables: doh, ray, me, fah, sol, lah, te, doh (Rev. John Curwen 1816-1869)
where each tone is given a name according to its relationship with other
tones in the key.
26.3.2.3 Musical scale, tones,
sharps and flats, equal temperament scale, musical instruments
See diagram 26.3.2.3: Staff notation of the
major diatonic scale
A series of musical notes is called a scale. The pitch interval for
most musical scales is the octave. In European music the octave is divided
into seven unequal parts called the major diatonic scale. The lowest
note is called the keynote. The eight notes are shown by letters. Pitch
intervals are called major tone, minor tone and limma. The note called
middle C, 264 hertz, is in the middle of the piano keyboard. The Chinese
music scale is divided into fewer parts.
Table 26.3.2.3
| Note |
"middle" C |
D |
E |
F |
G |
A |
B |
C |
| Relative frequency |
24 |
27 |
30 |
32 |
36 |
40 |
45 |
48 |
| Actual frequency, Hz |
264 |
297 |
330 |
352 |
396 |
440
pitch standard |
495 |
528 |
| Pitch intervals |
C: D 27/24 = 1.125 |
D: E 30/27 = 1.111 |
E: F 32/30
= 1.066 |
F: G 36/32 = 1.125 |
G: A 40/36 = 1.111 |
A: B 45/40
=
1.125 |
B: C 48/45
= 1.066 |
- |
| Tone |
9 to 8 Major tone |
10 to 9 Minor tone |
16 to 15 Limma |
9 to 8 Major tone |
10 to 9 Minor tone |
9 to 8 Major tone |
16 to 15 Limma |
- |
The difference between a major tone and minor tone, called a comma,
= (9 / 8) / (10 / 9) = (81 / 80). The difference between a minor tone and
a limma, called a diesis, = (10 / 9) / (16 / 15) = (25 / 24). Additional
notes to the major diatonic scale, called sharps and flats, raise or lower
a note by a diesis. Frequency of A sharp, A#, = 440 × (25 / 24) = 458.3
Hz. Frequency of A flat, Ab, = 440 × (24 / 25) = 422.4 Hz. Frequency
of G# = 396 × (25 / 24) = 412.5 Hz. Frequency of Gb = 396 × (24
/ 25) = 280.2 Hz. The scale of 22 notes containing all the sharps and flats
is called the chromatic scale. In an equal temperament scale the interval
between aa note and its octave is divided into equal pitch intervals, e.g.
twelve tone scale divides by 12 to give interval = x. Pitch interval of
octave = 2, so x12= 2, 12 log x = log 2, x = 1.059 (similar to
a limma, 16 / 15). This equally tempered scale based on A = 440 Hz pitch
standard. Note cases where similar note become mistuned to become the same
frequency, e.g. G# and Ab.
Table 26.3.2.3.1
| Note |
C |
C# Db |
D |
D# Eb |
E |
F |
F# Gb |
G |
G# Ab |
A |
A# Bb |
B |
C |
| Frequency |
261 |
277 |
294 |
311 |
330 |
349 |
370 |
392 |
415 |
440 |
466 |
494 |
522 |
26.3.2.4 Timbre (quality)
Different musical instruments may play the same note but sound different
because they have different quality.
26.3.2.5 Resonance in paper
pipe or drinking straw
See diagram 26.3.2.5
1. Use paper, scissors, tape, pencil. Cut a 15 cm × 15 cm square
of paper, and roll it tightly diagonally around a pencil. Use adhesive
tape on the centre to hold it together. Remove the pencil. At one end,
cut in the corner of the V one third of the way in, on both sides. If you
do not cut right from the corner of the V it will not work. Fold the triangular
end that you have marked down, and press it gently onto the pipe to make
it airtight. Place the other end of the tube in your mouth, and suck
gently. The triangle will vibrate sounding like a whistle. Make different
sizes of paper pipes and note how the sound varies. Note whether it makes
the same sound whether you blow gently or hard.
26.3.2.6 Resonance in aluminium pipe
The vibration of a pipe, caused due to being knocked, may drive the
wave motion of the air inside the pipe. The wave motion transfers and reflects
so that standing wave forms inside the pipe. This is the principle of
wind instruments, e.g. a flute. Its pitch may change through adjusting
the standing waves of the air column inside the pipe. Use a 1 m long,
2.5 cm of diameter, aluminium pipe. Hold the middle of the pipe horizontally
with your thumb and index finger. Knock the pipe on its middle as possible
with golf. listen to the sound of the pipe. Use a ruler to measure the
pipe, from its middle to the two sides, separate 13 cm, 25 cm, 35 cm
and 39 cm. Then mark them on the pipe with a sharp pencil or other pens.
Note that the positions marked are approximate. Real exact position must
be dependent on the resonance of the pipe. Press some point on the pipe
and knock it with the golf. If the pipe may sound the pure resonance, the
point is the exact position. Hold the pipe at the points marked separately
with your thumb and index finger vertically then knock it with the golf.
listen to the sounds and tell them. Holding the pipe and knocking it
causes its vibration so that a waving air column, i.e. a standing wave,
forms inside the pipe. The standing waveform depends on the position
at which the fingers hold the pipe and the position knocked. The positions
are different, the waveform is different and the frequency of the sound
is different. When knock the pipe at 25 cm from the middle of the pipe,
the pitch is the lowest (viz. the frequency is the lowest.); when knock
the pipe at 13 cm and 39 cm from the middle of the pipe, the pitch is the
highest (viz. the frequency is the highest.). The two ends of the above
pipe are open. At the open ends the incident wave and the reflected wave
are in phase with one another so the vibrations of the air at the ends
are strengthened. Thus both of the two ends are the antinodes of the standing
wave. Hold the pipe at different position and knock it thus the amount
of the standing waves are different so the pipe may sound different pitches.
The more the standing waves, the higher the pitch of the pipe. Find the
best positions to be knocked and the points at which the pitch of the pipe
is the highest and lowest by the same way. If plug up one end of the pipe,
at the end, the incident wave and reflected wave are out of phase [having
opposite phase] the point is the node of the standing wave.
26.3.2.7 Bottle xylophone
See diagram: 26.3.1.6 Bottle sounds
(Greek: xylos, wood)
Set up the bottles in a row. Partially fill each with water. Make sure
there is a different amount of water in each. Now tap each bottle in turn
and listen to the different pitch of each bottle. Arrange them in order
from highest to lowest pitch. Relate this to height of the water in the
bottle. Does the width of the bottle affect the pitch. Now blow across the
top of a bottle. Is the note the same as when you tapped the bottle? Vary
the amount of water in the bottle. Do the notes change the same way as when
you tapped against the bottle? Is it the column of air above the water or
the column of water which determines the note? Hint: think about the length
of the vibrating column of air in a wind instrument. Can you tune the bottles
to play a scale of music? Check your notes against a musical instrument.
26.3.2.8 Reed vibrations
Vibrating surfaces act in the same way as the reed in many musical
instruments
1. Hold a ruler tightly onto a table and pluck it in a downwards direction.
Listen to the sound.
2. Hold two sheets of paper together and blow into one of their sides.
Hold your lips tightly together and blow through them to make a funny sound.
3. Play a comb wrapped in tissue paper or a leaf. The reed starts vibrations
in a musical instrument's column of air. For the human voice, the vocal
cords in the throat act as a double reed and are set in motion by air
exhaled from the lungs.
26.3.2.9 Musical instruments
1. Aerophone (column of air vibrates to make the sound), e.g. flute,
trumpet, pipe organ, Australian aboriginal didgeridoo. Denser, harder timbers
produce a better tone as the sound wave travels more easily through them.
As an aerophone is played the air in the resonating column becomes warmer
and moister. Humid air is less dense than dry air. Warm air is also less
dense than cool air. With this double drop in the density of the air, the
notes become sharper or slightly higher. As the reed warms and moistens
more air is allowed to escape from the column and hence it becomes less
dense and the notes become sharper or slightly higher.
2. Chordophone (strings are vibrated), e.g. violin, guitar, piano.
As the strings warm their tension cases and the notes become flat or slightly
lower.
3. Idiophone (percussion instrument), e.g. cymbals, paired sticks,
lagerphone.
4. Membranophone (a membrane is vibrated), e.g. drums. Investigate
how different notes are produced on the different instruments. Look for
a resonator or vibrating system for each instrument.
5. The sound vibration may be free or maintained.
Free vibration occurs when just one sound is made and then allowed
to die out in time, e.g. plucking a guitar string or tapping a tuning fork
once.
Maintained vibrations occur when the vibrations making the sound are
continued, e.g. scraping a bow across the strings of a violin and playing
a long note on a bugle.
6. Notes are created by altering the length and/or mass of the string.
or by altering the length of the air column. The energy comes from the hands,
arms or breath of the player. The resonator is the string, column of air
or membrane.
7. Sounds are radiated by a variety of means. Stringed instruments
use the timber body of the instrument, some woodwind and brass instruments
have bell shaped openings that radiate the sound, flutes and piccolos use
their holes and hence produce very little sound. Each of these methods is
called an impedance resonator. Percussion instruments do not need impedance
resonators since the object hit is large enough to move enough air to produce
an audible sound.
26.3.2.10 Musical notes,
wind instruments
See diagram 26.5.1
The air column inside the pipe may generate standing waves so that
the pipe emits / gives off harmonious sound as meeting the certain condition.
Use two glass tubes, one with an end open, another with two ends open;
a signal generator; a small loudspeaker; two pieces of leads; a ruler.
26.3.2.11 Pan pipes
Cut a strip of corrugated cardboard about 60 mm wide and 150 mm long
so that the corrugations run along the short distance. Push a straw through
every second opening of the cardboard. Cut each straw to a different length,
the longest at one end and the shortest at the other, with even changes
of length in between. Blow across the tops of the straws to make a sound.
Tune the instrument by cutting the length of each straw so that a musical
note can be played.
26.3.2.12 Drinking straw
oboe and trombone
1.1 Pinch flat 1 cm at one end of a paper drinking straw or paper tube.
Cut off thin little triangles from each side so that the drinking straw
has an arrow shape. These make the reeds. Put the straw far enough into
your mouth so your lips do not touch the corners but are around the round
uncut part of the drinking straw. Press gently with your lips on the straw.
Blow gently just past the cut. Move the end of the drinking straw in and
out of your mouth until you get a sound. While you are blowing try to touch
the cut ends with your tongue and feel them vibrating.
1.2 If you do not get a sound, try keeping the cut ends together with
your tongue and blow again. If you still do not get a sound the cut ends
may be too stiff. Remove the straw and press the cut ends together or manipulate
them to make them less stiff.
1.3 Cut three small slits along the length of the straw about 2.5 cm
apart. Cover one of them and blow as before. Separate the slits so they
form small holes. Then cover two, then three each time you blow. Put three
fingers of the left hand on the farthest three holes and three fingers of
the right hand on the nearest three holes. The length of the air column vibrating
to form a sound is as long as the nearest open hole.
1.4 repeat the experiment with different lengths of drinking straw.
2. Hold two or more sheets of paper together and blow into one of their
sides. Hold your lips tightly together and blow through them to make a
"raspberry" sound. Play a comb wrapped in tissue paper or a gum leaf. The
vibrating surfaces of the lips, the sheets of paper or the ruler act in the
same way as the reed in many musical instruments. The reed may be constructed
of metal or cane in the case of woodwind; it may even be organic as in some
brass instruments, the didgeridoo and the human voice. The reed initiates
the vibrations in each of these instruments' column of air.
3. Pinch flat 1 cm at one end of a drinking straw. Cut off little triangles
from each side. These make the reeds. Put the straw far enough into your
mouth so your lips do not touch the corners. Press gently with your lips
on the straw. Blow gently just past the cut. Move the end of the drinking
straw in and out of your mouth until you get a sound. Slide a wider drinking
straw or plastic tube over the drinking straw you are blowing into. The
second tube can be used to lengthen or shorten the length of column of vibrating
air, just like a trombone.
26.3.2.13 Humming paper
tube
See diagram 26.2.13
Use a 20 cm square piece of paper. Cut off one corner. Cut two notches
in the opposite corner. Roll the paper diagonally to make a tube about as
thick as a pencil. Fold the notched corner to cover the opening. Suck through
the tube. You can hear a humming sound. The paper corner outside the notches
is drawn in then starts to vibrate slowly making a deep note.
26.3.2.14 Blow pieces of
drinking straw
See diagram 26.2.14
1. Hold a piece of drinking straw against your lower lip and blow across
the open end with your lips close together. Note the tone of the sound
produced by the open drinking straw. Close the end of the drinking straw
with your finger and blow again. The tone from the drinking straw when the
end is closed is about an octave lower than when the end is open. Repeat
the experiment with a shorter drinking straw. When vibrating air changes
the tone by an octave the air is vibrating twice as fast as before. So the
air was vibrating twice as fast in the open straw as in the closed straw.
The shorter the column of air the higher the sound because air vibrates faster
in a a short column than in a long column. So the pipes of an organ, e.g.
a church organ or town hall organ are different sizes and lengths. The highest
sounds come from very small pipes and the lowest sounds come from very large
pipes.
2. Cut a 2 cm piece from a plastic drinking straw. Press one end together.
Cut it to a point. Put it against the front of your top palate. Make
musical sounds when you blow through it. The pointed tongues of the straw
vibrate rapidly as the air passes through the piece of straw to make
a high note. Many musical instruments are based on this principle of
a vibrating reed.
3. Blow different lengths of drinking straws. Flatten 2 cm of the end
of a straw. Cut off the end corners. Use your lips to hold the end of the
straw flat. Blow into the straw to make a sound. Do not blow too hard or
you may hyperventilate (too much oxygen to the brain). If you feel dizzy
breathe into a paper bag for a few minutes. Cut other straws to different
lengths. Blow into each to make a sound and arrange them in order from low
to high pitch. Observe the lengths of the straws and the pitch of the sound.
26.3.2.15 Bunsen burner
trombone
Use two glass or hard plastic tubes 50 to 100 cm long with one tube
diameter greater than a Bunsen burner tube but less than the second tube.
Light the Bunsen burner. Hold the smaller diameter tube vertically over the
flame then move it up and down until you can hear a resonance sound. Hold
the greater diameter tube vertically around the first vertical tube. You
can move it up and down to change the pitch of the resonance. The resonance
e is produced by the sudden expansion of air in the tube.
26.3.3.3 Tuning forks
A tuning fork is bar of steel shaped like a U with a handle. When you
strike a prong of the fork lightly struck on a suitable surface, e.g. felt
pad or rubber bung, and put the handle in contact with a wooden surface,
you hear a pure note of constant frequency. This frequency is usually stamped
on the handle. If you strike the fork on a hard surface, e.g. the bench,
you hear an impure note. Examine a set of vibrating tuning forks. Note how
do their lengths and thickness correlate with their pitch when struck.
26.3.3.4 Sound wave patterns
of a tuning fork, waveform of a tuning fork
See diagram 26.191: Wave pattern of a tuning
fork | See diagram 26.1.1: Vibration of tuning
fork | See diagram 26.1.2: Harmonics
1. With a few drops of hot sealing wax attach a piece of fine wire
to the prong of a tuning fork. The fork is held rigidly by the handle and
placed horizontally just above the table top. Smoke a small pane of glass
over the flame of an oil lamp or a candle. Now lay the smoked glass pane
under the prong with the fine wire bent to touch the glass pane. Start the
vibrations with the finger and draw the pane along the table fast enough
to make a wavy line on the pane. Repeat this experiment drawing the pane
away at different speeds and using different tuning forks.
2. To describe the graph of the amplitude of the tuning fork against
time, glue a short thin stiff wire to the end of a tuning fork with drops
of candle wax. Prepare a stand and a table of fit height. Fix the tuning
fork on the stand, making sure the tuning fork is just above the tabletop.
Get a block of glass board and blacken one side of the glass board by fuming
it with the smoke and fire of a candle. Place the glass board under the
tuning fork, the black side upwards. Bend the thin lead to make its peak
touch the glass board just. Now the tuning fork is at rest. Pull the glass
board and the lead draws a straight line on the glass board. Strike the
tuning fork to start its oscillation. Pull the glass board at fit speed.
The lead draws the waveform on the glass board. See the lower diagram.
Repeat the experiment but pulling the glass board at different speeds
or using different tuning forks.
3. Tuning forks make a pure note when struck and allowed to vibrate.
This note is of just one frequency and is called the first harmonic of
that frequency. A musical instrument playing the same note makes not only
the pure note of the tuning fork but also other notes called harmonics.
Harmonies are notes whose frequencies are an integral number of times
the frequency of the first harmonic. Thus the second harmonic is twice
the frequency of the first. It is the combination of many harmonics that
give musical instruments their distinctive sound. Tap the tuning fork and
listen to the sound it makes. Now play the equivalent note on a piano or
other musical instrument. Do they sound the same? How do the sounds differ?
26.3.3.5 Tuning forks automatically move ping-pong
balls
See diagram 26.1.3
Fix two identical tuning forks on two identical resonance boxes. Hang
a ping-pong ball from the arm of a stand with a string, so that i it just
touches a tine of one tuning fork. Place the resonance boxes mouth to mouth.
Use a rubber hammer to knock another tine of the tuning fork, not touching
with the ping-pong ball. Observe the change in motion of the ping-pong ball
as it statrs to vibrate. It changes from being at rest to vibrating, showing
that it has gained energy. The knocked tine of the tuning fork, as a sound
source, causes the change in motion of surrounding medium.
26.3.6 Slide whistle, piston
flute
See diagram 26.3.2: Slide whistle
A short duct cylindrical flute with a sliding piston and handle so
is closed at one end.
26.3.7 Glass harmonica
See diagram 26.3.7: Glass harmonica
Use 6 light weight glasses. Fill them with different amounts of
water. Dip you index finger in water then move it slowly around the rim
of one of the glasses to create a sound. Repeat the experiment with the other
glasses and observe that the tone of the sound depends on the amount of water
in the glass, i.e. the volume of air in the glass above the water. The sound
has a ringing tone but some people think it is a haunting sound and do not
like it. You could tune a set of glasses to make a musical instrument and
many composers have written music for the glass harmonica.