School Science Lessons
26. Sound, resonance, pitch, tuning fork, oscillation, vibration
2012-01-28 SP
Please send comments to: J.Elfick@uq.edu.au
Table of contents
26.0.0 Sound
4.93 Sound, experiments, UNESCO
26.8.0 Interference and diffraction
of sound, beats
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
26.3.1 Resonance in strings
26.9.0 Sound reproduction, microphone
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
26.2.0 Pitch, frequency
26.2.0 Pitch, frequency
26.2.4 Doppler effect, change in pitch
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
Order online: Sound tube, Resonance
tones from twirling
Order online: Singing rods, resonance
in an open rod
See pdf: Singing Bowl
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
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)
26.3.0.1 Singing drinking glass, wine glass,
water organ
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
26.3.3.3 Tuning forks
26.3.3.3 Tuning forks
26.3.1.5 Frequency of a tuning fork
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
26.1.9 Ping-pong ball hits vibrating drum
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. 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.
4. Sound waves can:
4.1 reflect, e.g. echoes,
4.2 refract, i.e. bend towards the normal when pass into media in which
their speed is slower,
4.3 diffract, e.g. you can hear people talking around the corner or on
opposite sides of a large tree trunk,
4.4. form interference patterns, e.g. beats.
5. 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.
6. 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.
7. 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.
8. 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 x wavelength.
9. 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.
10. 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.
26.1.1 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 Ping-pong ball hits vibrating drum
1. Tape the string to the ping-pong ball and hang it next to one side of
the drum. Gently hit the other side of the drum. At the same time measure
how far the ball bounces off the side of the drum. Now hit the drum harder.
Measure the distance again. Loudness or volume is determined by the distance
of the sound source from the car, the duration of the sound and the intensity
of the energy transmitted per unit area per unit of time.
2. Tape the string to the ping-pong ball and suspend it in a clear space.
Tap the tuning fork and place it next to the hanging ball. What happens?
Next tap the tuning fork and then just touch it on the surface of the bowl
of water. What happens? Now blow up the balloon. Pull the neck to make a
slit and let the air out of the balloon. What do you notice about the neck
of the balloon? Place the tin on the palm of your hand. Shout into its open
top. Feel the vibrations on your hand. 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? Tape the string to the ping-pong ball and suspend it in a
clear space. Tap the tuning fork and place it next to the hanging ball. What
happens? Next tap the tuning fork and then just touch it on the surface of
the bowl of water. What happens? Now blow up the balloon. Pull the neck to
make a slit and let the air out of the balloon. What do you notice about
the neck of the balloon? Place the tin on the palm of your hand. Shout into
its open top. Feel the vibrations on your hand. 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
am longitudinal compression waves and produce sound.
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 X 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.
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 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
X 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 Singing glass, water
organ
See diagram 26.3.0.1: Singing glass
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.
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
Find the frequency of a tuning fork with a set of tuning forks of known
frequencies
1. 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 = lambda
/ 4, lambda = 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 = lambda
/ 4, where lambda = wavelength of the tuning fork. When resonance occurs at
length AC = L2, then the column of air length (L2 + e) cm = 3 X lambda /
4.
L1 + e = lambda / 4
L2 + e = 3 X lambda / 4
(L1 + e = lambda / 4L) - (L2 + e = 3 X lambda / 4) = lambda / 2
Velocity of sound = frequency X wavelength, v = n X lambda, v = 2 X 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
The sonometer, monochord, is a hollow wooden with a moveable bridge, a
pulley at one end to allow a load to produce tension in a wire that passes
over two movable bridges A and B and a peg at the other one end. When you
pluck the wire between A and B at the centre the wire between the bridges
starts to vibrate and emits a musical note of definite frequency. You can
change this frequency by changing the load to change the tension in the wire
or by changing the distance between bridges A and B. You can "tune" the sonometer
to the sound of a tuning fork of known frequency by different methods.
1. 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.
2. 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.
3. 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
4. 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.
5. Prepare an open mouth plastic box instead of the above wooden board.
6. 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 X 25 mm X 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
Order online: Singing rods | Order online: Whirling sound tube
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.
| 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 x (25 / 24) = 458.3 Hz. Frequency
of A flat, Ab, = 440 x (24 / 25) = 422.4 Hz. Frequency of G# = 396 x (25 /
24) = 412.5 Hz. Frequency of Gb = 396 x (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.
| 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 X 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
Place two same tuning forks on two identical resonance boxes separately.
Hang a table tennis at the arm of a stand with a string, making sure that
the ball just touches a tine of one tuning fork. Place the resonance boxes
mouth to mouth and use a rubber hammer to knock another tine of the tuning
fork, not touching with the ball. Observe the change in motion of the ball.
The table tennis ball will vibrate. The ball changes from being rest to moving.
It shows it has gained energy. The knocked tine of the tuning fork, as a
sound source, causes the change in motion of surrounding medium, when its
energy transfers in the space. Especially it causes the resonance of another
tine to make the tine absorb the energy from the sound source furthest, and
it causes the vibration of the table tennis.
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, e.g. wine 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.