School Science Lessons
Sound, wave properties, musical instruments, ear and hearing
2009-09-15
Please send comments to: J.Elfick@uq.edu.au
See: Interesting websites
Table of contents
See 25.0: Waves
26.0.0 Sound
4.93.0 Different sounds
26.1.0 Wave properties of sound
26.2.0 Pitch, frequency
26.3.0 Resonance
26.3.1 Musical instruments, resonance in strings
26.3.2 Musical instruments, resonance in air columns
26.3.3 Tuning forks
26.4.0 Transmission of sound
26.5.0 Speed of sound
26.6.0 Ear, voice, hearing, voice, audible limits
26.7.0 Reflection and refraction of sound
26.8.0 Interference and diffraction of sound, beats
26.9.0 Sound reproduction
4.93.0 Different sounds
1.7 Knocking sounds (Primary)
1.16 Hearing sounds game (Primary)
2.7 Bottle sounds (Primary)
2.2 Bird sounds (Primary)
2.7 Bottle sounds (Primary)
3.12 String telephone (Primary)
4.7 How sound travels (Primary)
4.93 Sound wave patterns
4.94 Wave patterns of a tuning fork
4.95 Seeing and feeling vibrations that make sound waves
4.96 A bell from a spoon
4.97 Vibrating cans, string telephone
4.97.1 Goose horn tube
4.97.2 Kazoo tube
4.97.3 Comb kazoo
4.98 Sound waves travel through wood
4.99 Materials that absorb sound
4.100 Sound cannot travel through a vacuum
4.101 The ear and hearing
4.102 The voice and speaking
26.1.0 Wave properties of sound
26.1.0.1 Sound cannot travel through a vacuum
26.1.1 Sound wave patterns, oscillations, origin of sound, tuning fork vibration
26.1.2 Oscillation of an object and production of sound
26.1.3 Oscillation of a ruler, vibrating rulers
26.1.4 Oscillation of grains
26.1.5 Oscillation in your throat
26.1.6 Oscillation of a tuning fork in water
26.1.7 Oscillation of a soap film
26.1.9 Ping pong ball hits drum
26.1.10 Seeing and feeling vibrations that make sound waves
26.1.11 Vibrating cans
26.1.13 Vibrating desk, blackboard, chalkboard
26.1.14 Feel vibrations with a balloon
4.86 Ripple tank
4.87 Circular pulses
4.88 Straight pulses
4.89 Reflection at a straight barrier
4.90 Reflection at a curved barrier
4.91 Refraction of waves
4.92 Diffraction in a ripple tank
4.93 Sound wave patterns
4.94 Wave patterns of a tuning fork
4.95 Seeing and feeling vibrations that make sound waves
4.96 A bell from a spoon
4.97 Vibrating cans, string telephone
4.98 Sound waves travel through wood
4.99 Materials that absorb sound
4.100 Sound cannot travel through a vacuum
4.101 The ear and hearing
4.102 The voice and speaking
26.3.1.6 Velocity of sound in air
26.2.0 Pitch, frequency
26.2.1 Pitch and length, see and feel vibrations that produce sound, pitch
26.2.2 Pitch and tension
26.2.3 Whirling pipes, pitch and length
26.2.4 Doppler effect
26.2.5 Hanging buckets
26.2.6 Thin and thick strings
26.2.7 Stretched rubber band
26.3.0 Resonance
26.3.0.1 Singing drinking glass, wine glass, water organ
26.3.0.2 Insect footsteps in a paper bag
26.3.0.3 Spray from "fish wash" dishes in Chinese temples "frictionizing" the brim, stationary waves
26.3.0.4 Amplify sound from comb, comb resonator, chimes
26.3.0.5 Use a drink-can to amplify the sound of a thread
26.3.0.6 Tap different containers
26.3.0.7 Cellophane noise
26.3.0.8 Knocking sounds
26.3.0.9 Pitch from knocking on and blowing over bottles
26.3.1 Musical instruments, resonance in strings
26.3.1.1 Paper rider thrown off
26.3.1.2 String resonates with tuning fork
26.3.1.3 String vibrates under constant tension
26.3.1.4 String vibrates at constant length
26.3.1.4.1 Violin strings and piano strings
26.3.1.5 Frequency of a tuning fork
26.3.1.6 Velocity of sound in air
26.3.1.7 Frequency of a tuning fork
26.3.1.8 Piano resonance
26.3.1.9 Monochord, sonometer
26.3.1.10 Pitch and mass
26.3.1.11 Plastic bottle guitar
26.3.2 Musical instruments, resonance in air columns
26.3.2.1 Wind instruments
26.3.2.2 Octave and pitch, sol-fa (solfege) syllables
26.3.2.3 Musical scale
26.3.2.4 Timbre (quality)
26.3.2.5 Resonance in a paper pipe or a drinking straw
26.3.2.6 Resonance in aluminium pipe
26.3.2.7 Bottle xylophone
26.3.2.8 Reed vibrations
26.3.2.9 Investigate musical instruments
26.3.2.10 Musical notes, wind instruments
26.3.2.11 Pan pipes
26.3.2.12 Drinking straw oboe and trombone
26.3.2.13 Humming paper tube
26.3.2.14 Blow pieces of drinking straw
26.3.2.15 Bunsen burner trombone
26.3.2.16 Bottle sounds
26.3.2.17 Knocking sounds
26.3.3 Tuning forks
4.94 Wave patterns of a tuning fork
26.3.3.4 Sound wave patterns of a tuning fork, waveform of a tuning fork
26.3.3.5 Tuning forks automatically move ping-pong balls
26.3.1.5 Frequency of a tuning fork
26.3.1.7 Frequency of a tuning fork
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 26.1.0: 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. 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.
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.
26.1.0.1 Sound cannot travel through a vacuum
The speed of sound in air at 0oC = 331 ms -1. Use an aspirator or simple vacuum pump to pump the air from a large jar or a bell jar fitted with a spigot. Use a bicycle pump to make a simple vacuum pump. Open the pump and remove the piston. Unscrew the bolt that holds the leather washers then reverse the washers by turning them over. Replace the washers on the piston and reinsert the piston in the pump cylinder. Suspend a small bell from fine threads inside the jar or bottle and shake the bell while the jar is filled with air. You can hear the bell ringing quite clearly. Use the aspirator or simple air pump to remove as much air as possible from the jar. Shake the bell again. The sound of the bell is not as loud as before because sound cannot travel through a vacuum.
26.1.1 Sound wave patterns, oscillations, origin of sound, tuning fork vibration
See diagram 26.1.1a: 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 an 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 a 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 in 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 a 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 a 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 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 Seeing and feeling vibrations that make sound waves
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. Feeel the vibrations in the balloon.
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 sharness of flatness used by a group of musicians plavying 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
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
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
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
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
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.
26.3.0 Resonance, standing waves (stationary waves) in a string, standing waves in air columns, end correction
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
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 Use a 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 Pitch from knocking on and blowing over bottles
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.
26.3.1 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, resonance condition on a string, standing waves of the string, sonometer
See diagram 26.1.12
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 under 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 sqrt 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 sqrt T (X axis). If the points on the graph are in a straight line passing through the origin, n is proportional to sqrt 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 sqrt T/m cycles per second
26.3.1.6 Velocity of sound in air
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
26.3.1.7 Frequency of a tuning fork
To find the frequency of a tuning fork, knowing the value of the velocity of sound in air, do the previous experiment.
26.3.1.8 Piano 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, pitch and frequency, many notes from one 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)
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
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 Musical instruments, resonance in air columns
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
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 hettz, 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 a paper pipe or a 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
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 Investigate 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 26.1.2d: 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.