UNPh26a

School Science Lessons
Sound, wave behaviour of sound 2
2009-05-21
Please send comments to: J.Elfick@uq.edu.au
See also: Interesting websites

Table of contents
26.4.0 Transmission of sound, speed 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

26.4.0 Transmission of sound
26.4.1 Sound cannot travel through vacuum
26.4.2 Sound travels through an air column
26.4.4 Listen to a spoon
26.4.5 Sound travels in straight lines
26.4.6 Materials that absorb sound
26.4.7 Sound waves travel through wood
26.4.8 Listen to a fork
26.4.9 Sound vibrations extinguish a flame
26.4.10 Sound vibrations passing through a cylinder
26.4.11 Sound travels along a wire fence
26.4.12 How sound travels
26.4.13 String telephone
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
1.7 Knocking sounds (primary)
1.8 String sounds (primary)
1.16 Hearing sounds game
3.12 String telephone (primary)

26.5.0 Speed of sound
Velocity of sound in gases, liquids, and solids
26.5.1 Speed of sound with closed resonance tube
26.5.2 Speed of sound with a tuning fork
26.5.3 Speed of sound with a drum
26.5.4 Speed of sound with echoes
26.5.5 Speed of sound in solids
26.5.6 Speed of sound in liquids
26.5.7 Speed of sound in liquids with bubbles
26.5.8 Thunder and lightning

26.6.0 Ear, voice, hearing, voice, audible limits
4.101 The ear and hearing
4.102 The voice and speaking
26.6.1 Tones
26.6.2 The ear, how the ear works, model of the ear
26.6.3 Binaural hearing
26.6.4 Direction of sound, direction judgement of the ear
26.6.5 Range of hearing
26.6.6 Pitch of musical bottles
26.6.7 Siren
26.6.8 Musical saw
26.6.9 Savart wheel
26.6.10 Intensity and attenuation with a decibel, dB, meter
26.6.11 Attenuation of materials
26.6.12 Reverberation time for architectural acoustics
26.6.13 Ripple tank acoustics
4.86 Ripple tank
26.6.14 How the voice is produced, music perception and the voice
26.6.15 Sing and whistle octaves
26.6.16 Subjective tones
26.6.17 Difference tones and beats
26.6.18 Circular glockenspiel
26.6.19 Musical scale
26.6.20 Tuning forks on resonance boxes
26.6.21 Microphone and oscilloscope

26.7.0 Reflection and refraction of sound
26.7.1 Reflection of sound
26.7.2 Echoes in tank theatre
26.7.3 Balloon as a sound lens, acoustic lens

26.8.0 Interference and diffraction of sound, beats
26.8.1 Beats, superposition of waves of different frequencies
26.8.2 Interference of sound waves with tuning forks
26.8.3 Superposition of waves of equal frequencies with tuning forks
26.8.4 Superposition of waves of equal frequencies with loudspeakers
26.8.5 Wave interference in water, drop stones in water
26.8.6 Loaded tuning fork
26.8.7 Resonating objects have same frequency as source of vibration
26.8.8 Energy transfer between pendulums by resonance

26.9.0 Sound reproduction, loudspeakers, microphones, amplifiers, recorders
26.9.01 Transducer, carbon microphone in a telephone
26.9.1 Direction of sound, microphone
26.9.2 Microphone and loudspeaker
26.9.3 Record sound with a cassette recorder, compact disc and microphone
26.9.3.1 Analogue recording and digital recording
29.9.4 Use a hand lens to examine the grooves in a vinyl disc gramophone record
26.9.5 Glass tube with an open end, using signal generator

26.4.0 Transmission of sound, echo, absorption, transmission, string telephone, sound insulation, soundproofing, acoustics, baffles
When a periodic disturbance occurs in air, longitudinal sound waves spread out from it in three dimensions, just like the water waves that spread out from a vibrating source in two dimensions. The air in the path of a sound wave becomes alternately denser and rarer. These changes in pressure cause our eardrums to vibrate with the same frequency to produce the sensation of sound. The speed of sound in air is 332 m / sec at 0^oC. The speed of sound increases by about 0.2% for each 1^oC rise in air temperature.

26.4.1 Sound cannot travel through a vacuum
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.
2. Use a large wide mouthed bottle with a rubber stopper. Drill a hole on the stopper and insert a short glass tube into the hole. Use a small radio. Turn on the radio and turn up the volume to the maximum. Open the bottle and put the ratio into it. Cover the bottle with its stopper again and connect the glass tube on the stopper to an air pump with a rubber tube. Fill the seaming with some oil. Draw the air out of the bottle and listen to the sound from the radio at the same time. The sound is silent, soft and loud. If there is a fit screw clamp, nip the rubber tube with the clamp before drawing out the air. Repeat the experiment screwing the clamp tightly after drawing the air out of the bottle and using the clamp to control the speed at which air enters into the bottle after removing the air pump from the rubber tube. The process of sound's change may be displayed more obviously. If no fit radio, tie a small bell to a piece of very short string then put the bell into the bottle. Make sure that the length of the string is fit so that the bell does not touch the wall of the bottle when shake the bottle. Repeat the experiment shaking the bottle. You may see the bell waggling but you may not hear the sound from the bell firstly and gradually you may hear the sound and finally the sound recovers completely.

26.4.2 Sound travels through an air column
1. Put the end of the handle of a funnel into your ear. Be careful not to harm your eardrum. Listen to the every sound in the classroom. You may hear various sounds even whispers between students. Use a PVC tube of length about 50 cm. Insert the tube into a small funnel. It may be used a simple stethoscope. Press one end of the tube close to your ear and place the funnel on a mechanical watch. You may hear the "tick tick" sound the watch emits clearly. Bend the above PVC tube slightly then put it on your chest. You may hear your heart's palpitation. Here the stethoscope made by you has the same principle with that doctors use. Through stethoscopes doctors listen attentively to palpitations, breaths and any sounds patients' chest emit.
2. Fit the plastic tube over the small opening of the funnel. Place the large opening of the funnel over your heart or stomach and listen in at the other end of the plastic tube. See how many different body sounds you can identify from inside your body.

26.4.4 Listen to a spoon
See diagram 26.4.4
1. Use 1 metre of cotton cord. Hold both ends together and, in the loop so formed, balance a teaspoon. Now press both ends into your ears with your finger tips and bend down so that the string and fork hang freely. If you hit the spoon lightly with another spoon, you can hear a chime like a bell. Sound waves have travelled along the string to your ears.
2. To compare sound's travelling along solid and in air, tie a stainless steel spoon to the midpoint of a string of length about 1 m. insert the two ends of the string into your ears. Bend to make the spoon overhang free. Shake the string to knock a metallic object or let other person to knock the spoon with a metallic object. Listen the sound along the string. Knock again after leaving the ends of the string off your ears. Compare the sounds. Press your ear close to a tabletop then knock the table. Listen to the sound through the table. Leave your ear off the tabletop then knock the table again. Listen the sound from the air. Describe the difference between the sounds. Record your sound on a tape then play it. You may find that it is different from your ordinary sound. If you record other people's sounds then play them, the effects are the same. Discuss the reason. When the sound travels in different medium, the difference in speed and energy of the sound is remarkable. The speed and loudness of sound is much greater in solid than in air.
3. Use a 1 metre long string. string. Tie the middle of it around the handles of 4 to 5 spoons so that when you hold up the two end s of the string the spoons bang on each other. Push the ends of the sting into your ears, shake your head, and hear the chimes

26.4.5 Sound travels in straight lines
In a piece of poster board or construction paper, cut a strip out about 20 cm wide and 1 m to a paper tube. Place a clock at one end of the paper tube. Through another end of the paper tube listen to the "tick tick" the clock emits. It is clearer than in air. It shows that sound travels along straight lines.

26.4.6 Materials that absorb sound
Test the sound absorbing properties of small pieces of rubber, sponge, felt, and other materials. Place the piece to be tested on a wooden table top, strike a tuning fork, and bring its handle down on a piece of material. Then strike the tuning fork again and touch its handle on the bare wood top. Which is louder? Try each material.

26.4.7 Sound waves travel through wood
To show that sound waves travel through wood, rest the ear against one end of a table top and gently tap the other end of the table with a ruler or pencil.

26.4.8 Listen to a fork
Tie a fork in the middle of a piece of string about a yard long. Wind the ends several times around your forefingers and hold the tips of your fingers in your ears. Let the fork strike a hard object. If the string is then stretched, you will hear a loud, bell like peal. The metal vibrates like a tuning fork when it strikes the hard object. The vibration is not carried through the air in this case, but through the string, and the finger conducts it directly to the eardrum. Tie a fork in the middle of a piece of string about a yard long. Wind the ends several times around your forefingers and hold the tips of your fingers in your ears. Let the fork strike a hard object. If the string is then stretched, you will hear a loud, bell like peal. The metal vibrates like a tuning fork when it strikes the hard object. The vibration is not carried through the air in this case, but through the string, and the finger conducts it directly to the eardrum.

26.4.9 Sound vibrations extinguish a flame
Cut the base off a plastic drink bottle. Stretch a thin sheet of plastic or rubber over the cut base and secure it with an elastic band around the base. Light a small birthday cake candle. Hold the opening of the plastic drink bottle near the lighted candle. Strongly tap the plastic sheet at the other end. The vibration can extinguish the flame.

26.4.10 Sound vibrations passing through a cylinder
Hold a ticking watch to your ear. Then move it further and further away until you can just no longer hear it. Note the distance between the watch and your ear when you can no longer hear it. Make a cylindrical roll of paper about the same distance in length. Hold the paper cylinder to your ear then hold the ticking watch at the end of the roll of paper. You can now hear the watch ticking. When you first heard the watch ticking vibrations travelled out from the watch in all directions. When sound vibrations were trapped in the roll of paper they could not move in all directions, saved some energy and so the vibration move a longer distance through the cylindrical roll.

26.4.11 Sound travels along a wire fence
Divide into two groups and position yourselves as far apart as possible along a wire fence. You should still be able to see the other group. Watch the other group strike the wire. Time how long it takes for the sound to reach you in the air. Now place you ear on the wire of the fence and listen and time it again. If a long enough fence is not available listen to faint sounds travelling through a table or other solid object. You can hear sounds through the table that you may not hear through the air since the sound is travelling faster and therefore does not die out in as short a distance.

26.5.0 Speed of sound, velocity of sound in gases, liquids, and solids, resonance tube, Kundt's tube, effect of pressure, temperature, wind, shock waves, sonic boom
Sound travels faster in solids than in liquids than in gases. The speed of sound in gases increases with temperature.
In an ideal gas of molecular mass M and absolute temperature T, the speed of sound v = sqrt LRT / M, where R is the gas constant, and L is the ratio of specific heats (about 1.67 for monatomic gases (He, Ne, Ar), and 1.40 for diatomic gases (N₂, 0₂, H₂). The speed of compression waves in solids, v = sqrt (Young's modulus / density). The speed of compression waves in liquids, v = sqrt (bulk modulus / density). Sound is the physiological sensation received by the ear, originating in a vibration (pressure variation in the air) that communicates itself to the air, and travels in every direction, spreading out as an expanding sphere. All sound waves in air travel with a speed dependent on the temperature, under ordinary conditions, this is about 330 m per second. In addition the sound speed is related to the elasticity and density of the medium. Sound waves travel the fastest in solid and the slowest in gas. Speed of sound in air is 331.5 m / sec at 0^oC and 344 m / sec at 20^oC. The speed of sound is independent of pressure, frequency, and wavelength but is proportional to the square root of the absolute (Kelvin) temperature. The speed increases with temperature by about 0.61 m / s for each 1^oC rise. Sound speeds v1 and v2 at absolute temperatures T1 and T2 are related by v1 / v2 = sqrt (T1 / T2). Sound travels faster in solids and liquids than it does in gases. The speed of sound in sea water is about 1.5 km / s at 20^oC.
When the speed of a source equals the speed of sound the wave fronts cannot escape the source. The wave form a large amplitude "sound barrier" that makes flight difficult. The term "sound barrier" or "sonic barrier" was used when pilots doing in high speed dives noticed that as flying speeds approached the speed of sound: aerodynamic drag increased unusually and lift and manoeuvrability decreased. When the speed of a source exceeds the speed of sound, the wave fronts lag behind the source in a cone-shaped region with the source at the vertex. The edge of the cone forms a supersonic wave front with an unusually large amplitude called a "shock wave". The shock wave is heard as a "sonic boom". Unlike ordinary sound waves, the speed of a shock wave varies with its amplitude. The speed of a shock wave is always greater than the speed of sound in the fluid and decreases as the amplitude of the wave decreases. When the shock wave speed equals the normal speed, the shock wave is reduced to an ordinary sound wave. The ratio of the speed of a moving object, v, to the speed of sound, c, in a fluid is called the Mach number in honour of Ernst Mach, 1838-1916. Mach 0.5 is half the speed of sound and Mach 2 is twice the speed of sound. Subsonic speeds have a Mach number between zero and one. Supersonic speeds have Mach numbers greater than one. The shock wave from a supersonic object is a cone composed of overlapping spherical wavefronts.

26.5.1 Speed of sound with closed resonance tube
See diagram 26.5.1
Measure the diameter of the resonance tube. Add water to the glass cylinder until 3 / 4 full. Hold the resonance tube vertically in the cylinder with one end in the water so the water seals one end of the tube. You can raise and lower the tube to vary the length of the air column in the tube. Strike the tuning fork with a rubber bung. Hold the vibrating tuning fork horizontally close to the open end of the tube. Move the tube and tuning fork up and down until the sound is best reinforced. If you find more than one position where reinforcement occurs move the tube up and down to find the shortest tube length that gives the loudest sound. Hold the tube in the position of best sound reinforcement and measure the distance L from the top of the resonance tube to the water. The length of the air column must be increased by 0.4 X diameter of the tube to correct for the air outside the top of the tube that vibrates with the air column in the tube. The corrected length of the air column = 0.4 X diameter + L. Repeat the experiment using a tuning fork of different frequency. Wavelength = 4 X corrected length of air column. Velocity of sound = frequency of tuning fork X wavelength.

26.5.2 Speed of sound with a tuning fork
1. A tuning fork can make the closed air column form a standing wave. Speed v of sound, v = frequency of the tuning fork X wavelength. Fix the a U-tube on the stand. Pour water into the two glass arms. Lift the right tube so that the surface of water in the left tube is just under point A, at the end of the left tube. Knock the highest frequency tuning fork with a rubber hammer to start its vibration. Put this tuning fork above the left tube. Lower the right tube to lower the surface of water at the left tube so that the air column between the end and surface of water in the left tube is lengthened. When the water surface goes down from point A to C, the sound reaches the maximum. It resonates with the tuning fork. The fundamental of the air column is the same as the frequency of vibration of the tuning fork. Measure and record the length l₁ of the air column AC here. Lengthen the air column AC further until you hear the resonance sound of the air column. Knock the tuning fork again to make it keep vibrating. Find the position of the second resonance point. Record the length l₂ of the air column AC. Record the frequency of the tuning fork and the room temperature. Calculate the speed of sound by: v = 2f (l₂ - l₁).
2. Repeat the experiment using other tuning forks and calculate the speed of sound.
3. Calculate the average of speed of sound and record as m / s. The point A at the open end is the antinode of the standing wave. Point C on the water surface is analogous to a fixed end is the node. The distance between the node and the antinode is odd number times of 1 / 4 wavelength.
l₁ + e = w / 4 corresponding to the first resonance point
l₂ + E = 3w / 4 corresponding to the second resonance point, where w is the wavelength of the tuning fork, E is the correction of length [E is used to adjusted the value of the length] because there is a short distance between the tuning fork and the end of left tube viz. The length of the air column is slightly larger than the length of AC. the first formula above minus the second minus may get rid of E and get. (l₂ - l₁) = w / 2. therefore w may be obtained. As v = fw, the speed of sound may be found.

26.5.3 Speed of sound with a drum
1. Use a large drum, a trundle wheel or long measuring tape. Arrange students, on a calm day, in a large open area, e.g. an oval or a quiet straight road. Hit the drum every half second using a watch or borrow a metronome from the music department or use a 1 metre long pendulum. Walk 50 metres away from the drummer then the drummer repeats the exercise. Walk another 50 metres and repeat. At about 170 metres from the drummer you can observe that the drummer is hitting the drum exactly as the sound is heard but after stopping one "extra" beat is heard. If you assume that the light reaching the observer travels instantaneously from the drummer, the distance travelled by sound in a half second about 170 metres. tells us the speed of sound is about 340 metres per second. Similarly a contestant in a race may start at the sight of the puff of smoke from the starter's gun and not wait for the sound to arrive. Also, this explains why thunder is heard after the lightning flash is seen although they occur virtually together. The extremely hot lightning bolt causes an explosive expansion of air around it.
2. Compared with the speed of sound, the speed of light is infinity, in air sound waves travel uniformly, viz. the speed of sound is a constant so it may be calculated applying the formula on reform motion. Use a drum or a wasted metallic pail, a piece of tape measure, a metronome or a single pendulum. Do this experiment at a silent and open playground. Beat the drum 2 times every second (6 times in all). It is better to use the metronome to control the beating rhythm to assure the interval coincident and exact. Discover the difference in time between beating the drum and hearing the drum. When observe and hear around the drummer firstly, you may see beating drum and hear the drum at the same time, at 50 m far away from the drummer secondly, you may see beating drum before hear the drum at the same time, but the difference in time is not large, at 100 m far away from the drummer thirdly, you may see beating drum before hear the drum at the same time, and the difference in time is obvious. Continue to see and hear. At 170 m far away from the drummer, you do not hear the drum when you see the first beating, you hear the first drum at the same time you see the second beating, you hear the second drum when you see the third beating, you may hear a "extra" drum at 0.5 s after the drummer finishes his beating. Put t = 0.5 s and s = 170 m into the formula v = st then get v = 340 m. this is the approximation of the speed of sound. At this experiment suppose that the speed of light is infinity, viz. the action of beating seen and the action of practical beating happens at the same time no matter how far away from the drummer. It will cause some error but very small. So the speed of sound obtained with the approximate method processes certain veracity. If there are 2 cellular phones, one around the drummer, another being carried at the observer, their loudspeakers may receive the drum at the same time because electromagnetic waves travel at the same speed with that of light. In a sail boat race, the contestants should all start as soon as they see the smoke from the starting gun, not wait to hear the sound of the gun.

26.5.4 Speed of sound with echoes
1. Clap your hands 100 m from a high wall. Keep clapping steadily until each clap coincides with the echo of the last clap. Use a stopwatch to record the time between these claps. Measure the distance from the wall. During the time between claps the sound travels twice the distance from the wall. The speed of sound in air at 0^oC is about 331 m / s.
2. You need two pieces of wood to make a clapping sound, open space and a vertical flat surface outdoors, e.g. wall of school building. Face the wall 20 meters from the wall and move very slowly backwards while clapping with the two pieces of wood pieces. When an echo of the clapping sound is heard measure the distance The minimum time interval that the human ear can detect between two claps is 0.1 second. When this interval between the clap and the echo is shorter than 0.1 second, no echo is heard, so you hear no echo when you stand too close to the wall. By moving slowly backwards away from the wall, an echo will be heard at a certain moment. At this moment the echo came back within 0.1 second, the distance between observer and the wall is measured (about 17 m), and the speed can be calculated from: distance sound travelled (2 x 17 m 9 34 m) divided by the time (0.1 sec) equals 340 m / sec. When the speed of sound is already known, an approaching storm's distance may be estimated by counting the seconds between the lightning and the thunder, and multiplying this by the speed.

26.5.5 Speed of sound in solids
1. This experiment shows how well sound travels through a solid or a liquid. Place one ear to the desk and tap the desk top with the end of a ruler. Note whether the sound is louder than when passing through the air. You can place your ear to the ground to hear animals or to railway lines to listen for approaching trains. Put your head under water while in a bath or swimming and tap the side. Ultrasound can be used to take a picture of an unborn baby. You can listen through a wall by placing an empty glass between the wall and your ear. The glass acts like a stethoscope.
2. Sound waves travel faster in solid and liquid than in air. The speed of sound is dependent on the medium. Press your ear close to a tabletop and gently knock the tabletop with an end of a ruler or the neb of ball point pen. You may hear the sound through the table clearer and louder than in air. American Indians press their ears close to the ground to listen attentively to wild animals' running from afar. If some one presses his ear close to a rail, he may hear the sound that train wheels bump against the rail at a distance. Repairmen often press one end of a stick (or a ruler, a screwdriver) on the outer covering of a running machine and press their ear close to the ruler thus they may hear the abnormal sound from the inside machine clear. These show that the sound waves travel better in solid than in air.

26.5.6 Speed of sound in liquids
Immerse your head into water at a basin or swimming pool then gently knock its wall with your hand and listen attentively to the sound. When your head is above the water, knock the wall of the basin with the same magnitude of force. Compare the sounds.

26.5.7 Speed of sound in liquids with bubbles
1. Observe the sound in a liquid. Pass bubbles through the liquid and note the pitch of the sound drops.
2. A heating element superheats water causing steam bubbles that pass out into the surrounding cooler liquid and collapse. The collapse makes shock wave the causes the "singing" kettle.

26.5.8 Thunder and lightning During a thunder storm if you see a lightning flash and hear thunder 5 seconds later then the thunder storm was 5 x 331.5 metres away from you. Since sound waves travel through the air at a rate of roughly one mile every 5 seconds, you can calculate the distance in miles away of a lightning bolt by dividing the number of seconds between the lightning flash and the thunder by 5. Why does the rumble of the thunder last so much longer than the lightning flash? Thunder is caused by the rapid expansion of air that is heated to very high temperatures along the entire length of the lightning bolt, which may often be a mile or more long. The sound waves from this explosion need different amounts of time to reach your ears, because some parts of the lightning bolt are farther away from us than others. After you hear the bang, which is delayed and weakened with increasing distance, you can often hear a weak rumbling sound, which is the reflected sound waves. Thunder is the noise of the sound wave caused by the sudden expansion of air massively heated by lightning. The reverberations or rolling of thunder is caused by reflection of the sound from different layers of air of different temperatures.

26.6.0 Ear, voice, hearing, voice, audible limits
See diagram 26.6.0: Harmonics
Acoustics, the ear, voice, hearing, voice, audible limits, direction of sound, sound locator, sound ranging, sense of sound, sound pollution, explosive sound
The human ear can detect sound waves with frequencies of about 20 to 20,000 hertz. This range is known as "sound", with infasound below the range and ultrasound above the range.
Loudness measures the human perception of sound. A sound wave of high intensity is perceived as louder than a sound wave of lower intensity, but the sensation of sound is proportional to the logarithm of the sound intensity for most individuals. Loudness level is defined by a scale corresponding to the sensation of loudness. The zero on this scale = the sound wave intensity, Io = 1.00 X 10^-12 W / m², corresponding to the weakest audible sound. The loudness level, beta, 10 log (I / Io). The decibel (dB) has no dimensions. Decibel, dB is the logarithmic unit used for human audibility measurements ranging from 1, just audible, to 120, just causing pain. The linear scale ranges from 1 to 10¹² change in sound pressure. A doubling of sound pressure corresponds to 6 dB. A doubling of sound loudness corresponds to a tenfold increase in sound pressure, 20 dB. A different decibel scale is used for measuring the output of audio amplifiers in terms of intensity. The normal ear can distinguish intensities down to about 1 dB. Often people use the word "musical sound" for something they want to hear, and "noise" for what they do not want to hear. A tuning fork emits an almost pure note of one frequency. Musical sound is made up of superposition of a set of fundamental and harmonics with different frequencies and amplitudes according to certain law. For example, consider two sounds, one a mixture of harmonics (frequencies related by integer ratios) and the other a mixture of frequencies with no integer relationship among them. The first sound will result in an identifiable pitch, that of the fundamental frequency, and is called a musical sound. The second sound, viz. noise, will have a much different quality, so different that it may not even have an identifiable pitch. Thus the difference between music and noise is a gross example of quality. The sound, transitory and declined quickly is an explosion.
Some animals can hear sounds in the ultrasound range, e.g. dogs, but the human ear is not able to hear them. Bats use sonar echoes to locate insects using sounds in the 20 to 50 kHz frequency range. Some insects have developed bearings in this range so that they can take evasive action. Bats that transmit at a higher frequency can catch smaller insects than bats that transmit at lower frequencies. Dolphins use clicks of ultrasounds to locate shoals of fish.
Echoing ultrasounds are used in underwater sonar and to detect cancers and check on unborn human foetuses. Different tissues reflect ultrasound differently so a computer can assemble a picture of the unborn baby.
High amplitude ultrasounds are used to clean metals, to fatigue test materials and to break up kidney stones. This is similar to loud sounds causing avalanches on steep slopes. Sonar echoes are used in ships to measure depth and detect under water objects. ASDIC was an early form of sonar, an abbreviation for Anti-Submarine Detection Investigation Committee. Short wave radio listeners use several scales to record the characteristics of the signal they hear from their loudspeakers and headphones, e.g. "SIO" Signal strength, Interference and Overall rating, "SINPO" with the addition of N and P for Noise and Fading.
Pitch of a note
The pitch of a sound is how high or low it sounds. As frequency of the vibration of particles increases, the pitch of a note is raised. Pitch is affected by the mass, the length and the tension of the vibrating medium. The frequency of a vibrating string is inversely proportional to its length. The frequency will be doubled for a string which is only half as long Frequency is also increased by an increase in tension. Four times the tension in the string will double the frequency it vibrates at. In addition frequency varies inversely as the square root of the string's density. When you increase the density of the string, you will slow down the vibration rate and decrease the frequency. Put a small v-shaped piece of paper on a stretched string or the string of a musical instrument. Pluck the string and note the motion of the paper V. Decibels and sound pressure for sound pressure range of 0 to 140 decibels.
dB (pressure Ear's response scale) Sound pressure units (Pa)
0 dB: 2 x 10^-5 Pa
10 dB: just audible, the sound of falling leaves
20 dB: empty broadcasting studio 2 x 10^-4 Pa
30 dB: soft whisper at 5 m
35 dB: quiet library
40 dB: bedroom, no conversation 2 x 10^-3 Pa
50 dB: very quiet
55 dB: light traffic at 15 m
60 dB: air conditioning at 6 m. 2 x 10^-2 Pa
65 dB: normal conversation
70 dB: light freeway traffic
75 dB: conversation noticeably difficult
80 dB: annoying sound level 2 x 10^-1 Pa
85 dB: pneumatic drill at 15 m
90 dB: heavy truck at 15 m
95 dB: very annoying
100 dB: loud shout at 15 m 2
105 dB: jet plane take-off at 600 m
110 dB: riveting gun close by
115 dB: maximum vocal voice without amplification
117 dB: discotheque at full blast
120 dB: jet take-off at 60 m 2 X 10 Pa
130 dB: limit of amplified speech
135 dB: painfully loud
140 dB: on aircraft carrier deck 2 X 10² Pa

26.6.1 Tones
In general, musical sounds are made up of a certain limited number of frequencies. A resultant wave includes a set of simple harmonic waves, in which the fundamental frequency, f1, is the lowest and nf1 is harmonics. A musical note has a characteristic pitch, loudness and quality. The pitch of a sound is related to its frequency of vibrations, the "highness" or "lowness". The pitch is dependent on the fundamental. The loudness of a sound depends on the ability of the ear to "hear", which depends on the movement of the eardrum as sound waves arrive. The bigger the movement of the ear drum, the stronger will be the signals sent to the brain, and the louder the sound you hear. The loudness is the psychological reaction to the intensity of a sound. Quality or timbre is another parameter related to the psychological reaction. The quality depends on the amount of the harmonics.

26.6.2 The ear, how the ear works, model of the ear
See diagram 2.197
Air vibrations enter the ear by the auditory passage formed at the base of the ear by the eardrum membrane. They set the eardrum in motion and, in doing so, set in motion the system of three little bones attached to it. By this means they reach a cavity in the bone called the inner ear. One part of the ear is shaped like a snail shell. Here is found the organ that receives the sound vibrations and is connected with the brain by the auditory nerve. Another part of the inner ear includes three small semicircular canals and serves to maintain equilibrium. It plays no part in hearing. Sound vibrations are normally transmitted to the snail shell shaped cochlea by the eardrum and the small bones. This causes a nerve message carried to the brain. They can also be transmitted by the bones of the skull, and you hear a sound if the waves reach the cochlea by either route. When a sound reaches your two ears, you can distinguish the direction from which it comes. If it comes from straight ahead, the vibrations reach both ears simultaneously and with the same strength. However if the source of the sound is on one side of us, one of your ears is further away from it and receives the waves less strongly and with a slight delay. The pinnae collect the sound and contributes to your sense of direction. Sound is transmitted from the auditory canal via the eardrum into the middle ear. In the middle ear small bones act as an impedance matching mechanism. This maximizes the. amount of signal that is passed on to the brain. The bones also magnify the vibrations of the eardrum. The. message is then passed into the cochlea and on to the nerve that takes the. message to the brain. The auditory canal is a tube of air that is able to vibrate and is closed at one end by the. eardrum.

26.6.3 Binaural hearing
Hold the ends of a long tube to each ear and have someone tap in the centre and then a few centimetres to each side.

26.6.4 Direction of sound, direction judgement of the ear
To identify the direction and position of sound cover your eyes with a piece of black cloth. Other students emit sounds at different positions at a classroom, e.g. shake a string of keys, rub a piece of paper. Describe each sound source and its direction and position. Repeat the experiment with various sound sources emitting the sounds at the same time. Human hearing can not only identify the directions and positions of a sound sources but also tell their characters. High frequency location depends on difference in intensity produced by the shadow of the head. Location of low pitched sounds depends on phase difference. Use a model stethoscope with one tube longer than the other.

26.6.5 Range of hearing
The range of human hearing is from about 20 vibrations per second to about 20, 000 vibrations per second, nearly 10 octaves. Use an oscillator driving an audio system to show the range of hearing. Use a set of good speakers. Use whistles, tuning forks to establish upper range of hearing. The Galton whistle can be adjusted to produce an intense sound into the ultrasonic range.

26.6.6 Pitch of musical bottles
Blow across a set of bottles with water levels adjusted to give a scale.

26.6.7 Siren
An air jet is directed at a rotating disc with holes. Air is blown through concentric rows of regularly spaced holes on a spinning disc. Change of speed of the disc changes frequencies but not intervals.

26.6.8 Musical saw
A card is held against a dull saw as the sawing speed is varied.

26.6.9 Savart wheel
A set of gears on a single shaft of a variable speed motor have the ratios of frequency and pitch. Hold a stiff cardboard against the rim of a spinning toothed wheel. Use wheels on the same shaft each with different numbers of teeth. A tooth ratio scale is a set of gears with teeth are mounted coaxially on a shaft connected to a variable speed motor Varying the speed shows intervals are determined by frequency ratios rather than absolute pitch.

26.6.10 Intensity and attenuation with a decibel, dB, meter
Use a decibel, dB, meter to measure the intensity at various ranges. A sound level meter is used to measure the instructor speaking.

26.6.11 Attenuation of materials
Put various materials between a sounding board and a tuning fork stuck in a block of wood. Examine various acoustical tiles acoustical tiles

26.6.12 Reverberation time for architectural acoustics
Record toy pistol shots in various rooms then find reverberation time at different frequencies. Clap hands to generate sound for reverberation time. Measure reverberation time of the classroom with a dB meter.

26.6.13 Ripple tank acoustics
Put cross-section models of various auditoriums in a ripple tank to show scattering and reflection.

26.6.14 How the voice is produced, music perception and the voice
See diagram 2.198
Mouth, teeth, tongue, throat and lungs are all used in the production of the voice. The sound is produced by vibrations of two thin sheets of membrane called the vocal cords, which are stretched across the sound chamber called the larynx. The larynx is the upper end of the windpipe and is found well back, at the base of the tongue. Here a trap door of cartilage called the epiglottis automatically drops down over the larynx when you swallow, so that no food will go through the windpipe. When the cords are stretched by the contraction of certain muscles in the throat, a narrow slit forms between them. It is when the air is forced through this narrow slit that the cords are forced to vibrate. This sets the air vibrating in the windpipe, lungs, mouth and nasal cavities. The vocal cords located in the throat act as a double reed and are set in motion by air exhaled from the lungs. The quality and tone of the sound depends on the size and shape of the resonating cavities such as the windpipe, the back of the throat, the mouth and other air filled parts of the head. 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. The quality and tone of the human sound depends on the size and shape of the resonating cavities such as the windpipe, the back of the throat, the mouth and other air filled parts of the head. Ventriloquists speak in the normal manner but with some modification of their speech. They allow their breath to escape slowly, narrow the glottis at the back of the throat, open their mouth as little as possible and retract the tongue while moving only its tip. The resultant pressure on the vocal cords diffuses the sound so that it appears to be coming from another source. The greater the pressure on the vocal cords, the greater the deception. Ventriloquists use a dummy with moving lips to aid in their deception that the sound they are making is not coming from themselves. Other animals including lions are able to "throw their voices".

26.6.15 Sing and whistle octaves
Whistle and sing into a three foot pipe and use the resonance to show your whistling range is much higher than your singing range.

26.6.16 Subjective tones
A toy whistle emits tones at 2081, 1896 and 1727 Hz. Subjective difference tones at 169, 185 and 374 Hz are clearly audible. subjective tones.

26.6.17 Difference tones and beats
Two pure tones produce beats or difference tones.

26.6.18 Circular glockenspiel
Play major minor augmented and diminished cords on a circular glockenspiel.

26.6.19 Musical scale
Why the note scale is the best equal tempered scale numerical investigation of scales. A pianist discusses piano tuning.

26.6.20 Tuning forks on resonance boxes
A set of four different tuning forks mounted on resonance boxes make the musical scale

26.6.21 Microphone and oscilloscope
Examine the output of a microphone on an oscilloscope while listening to it. Use a microphone and oscilloscope show that a tuning fork does not produce a pure sine wave but a fork on a resonance box does.

26.7.0 Reflection and refraction of sound, sound lens, reverberation, speaking tubes, whispering galleries, zones of silence, sound ranging, echo sounding
Sound is reflected from surfaces to produce an echo. Even in a room echoes are produced. However, no distinct echo is heard because not just one reflection of the sound occurs. Sound waves are reflected by hard surfaces but may be absorbed by soft surfaces. If the reflecting surface is within 10-15 metres of the sources of vibration the echo seems to join with the original sound which then sounds longer, a reverberation. Reverberations is part of the technology of acoustics which is used in designing concert halls. Rock bands partly need massive amplification techniques because of the poor acoustics in the venues in which they play. However rock band singers may not be trained to project their voices and the audience often wants to hear it very loud indeed.

26.7.1 Reflection of sound
See diagram 26.4.6
Like other waves, the reflection of sound obeys the law of reflection that the angle of incidence is equal to the angle of reflection. Roll two paper tubes of length about 80 cm with a piece of hard paper. Place a table near a wall. Place a large sound insulation board on the table upright to the wall but not touching the wall. At one side of the large sound insulation board place a tube against a wall forming an angle with the tube. Near the below end of the tube place a clock on the table. At another side of the large sound insulation board place another tube against a wall forming the same angle with the tube. Listen to the sound of the clock through the below end of the tube. Measure the original value of the angle between the tubes and wall. Adjust the angle until the listener hears the loudest sound. Measure the angle again. Compare the angle's values.

26.7.2 Echoes in a tank theatre
See diagram 26.4.9
Use a piece of poster board or construction paper, cut off a strip. Bend the paper strip into a circle then put them into a flume. Leave an entrance between the two ends of the paper strip then fix it. Pour some water in to the flume, the water surface lower than the paper strips. Place a pulse generator at the entrance to start the vibration of water. The water waves reflect on the paper "wall" and finally form echo. Draw the waveform of the echo you see on a paper.

26.7.3 Balloon as a sound lens, acoustic lens
See diagram 26.4.10
1. The speed of sound travelling in gas depends on the density of the gas. The denser the gas, the slower sound travels. Sound travels at about 340 metres per second in air and about 270 metres per second in carbon dioxide. So sound should be refracted towards the normal when it moves from air to carbon dioxide. Blow up a balloon. Hold it against a fairly loud source of sound. Place your hands or cheek against the balloon to feel the vibrations. You hear sounds when their waves hit and vibrate your eardrums.
2. A balloon under pressure has a higher index of acoustic refraction than the surrounding air, so it behaves as a sound lens. Use a balloon and a microphone to listen to distant conversations. Use a balloon and a tiny loudspeaker to project a sound beam to an individual listener. Put some dry ice, frozen carbon dioxide, in a balloon. Tie off the balloon and weigh it on a balance. Watch the "weight" change as the dry ice sublimes. When the balloon is fully inflated use it as a sound lens. Use an incoherent source of sound, e.g. running water. Use an oscilloscope and microphone to measure the speed of sound through the balloon filled with carbon dioxide then calculate the index of refraction and focal length for the higher frequencies.
3. Hold an inflated balloon 10 cm from a transistor radio. Squeeze the balloon between your two hands and note the feeling. Turn up the volume of the radio and squeeze as before. Note the difference in feeling.
4. Balloons filled with different gases either focus or defocus sound waves. Fill the balloon with helium, carbon dioxide or air. Place the balloon between a small speaker and a microphone and measure the microphones output. Carbon dioxide focuses the sound but helium defocuses the sound, with air of course there is no difference.
5. Inflate a balloon with your mouth then tie its mouth. Place the balloon between a watch and your ear and press close to each other. You may hear the "tick tick" the watch emits. There is more carbon dioxide in the gas you breathe out compared with air so the gas inside the blown-up balloon has bigger proportion of carbon dioxide than air. The balloon also contains water vapour breathed out. The gas inside the balloon is denser than air outside the balloon because carbon dioxide is denser than air. Sound travels more slowly in a denser gas so sound waves refract on the surface of the blown-up balloon to collect together, just like a lens. The sharper the curvature of the balloon lens the smaller its focal length. Pull strings attached to the surface of the balloon to vary the thickness of the balloon lens. As there are more sound signals arriving your ear your ear may hear very low sound more clearly.
6. Quiet or far away sounds are hard to hear because sound energy spreads out as it moves away from its source. However, by using a balloon filled with carbon dioxide gas, you can focus sound waves to create a loud spot! Put about 50 mL, of crushed dry ice into a glass soft drink bottle. Stretch the neck of a round balloon over the top of the bottle. As the dry ice warms, carbon dioxide gas slowly fills the balloon. If you prefer, place the bottle in warm water to speed up the filling process. When full, remove the balloon and tie the neck to prevent carbon dioxide gas escaping. You now have a "lens" which you can use to focus sound. Balance the balloon on a coffee mug. About one metre away on one side of the balloon, place a radio (or other sound source) with the volume control turned down so that it is only just audible. Move your ear around on the opposite side of the balloon. At what point is the sound loudest? What happens if the balloon is removed when your ear is at that point? What happens to the loud point when you move the radio closer or further away from the balloon? Note: Carbon dioxide gas molecules slowly pass through the sides of the balloon, therefore you should fill the balloon just before using it.

26.8.0 Interference and diffraction of sound, beats, stereophonic sound, interference of sound waves using an air column or a stretched vibrating string
See diagram: 26.4.6
Sound waves show reflection, e.g. echoes, refraction, i.e. bend towards the normal when pass into media in which their speed is slower, diffraction, e.g. you can hear people talking around the corner communicate easily by speech, even when on opposite sides of a large tree trunk, and form interference patterns, e.g. beats.
Use 3 sound insulation boards with the same size. Drill a hole at the centre of each board. Upright place the 3 boards parallel to one another. Adjust their positions to make the 3 holes at one straight line. Place a watch outside of the hole on the first board and press your ear close the hole on the third board. You may hear the "tick tick" the watch emits clearly. It shows the sound travels to the ear directly through 3 holes. Move the middle board a bit to make the 3 holes not at a straight line. Although the sound does not travel to your ear directly but you may hear the sound still because the sound waves may round the obstacle to go ahead.

26.8.1 Beats, superposition of waves of different frequencies
See diagram: 26.8.4.4
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. Two beats per second will occur with combined frequencies of 200 Hz and 198 Hz. Sound waves reflect, e.g. echoes, refract towards the normal in media in which their speed is slower, diffract, e.g. you can communicate easily by speech even when on opposite sides of a large tree trunk, and form interference patterns, beats. You hear different frequencies of vibration as differences in pitch, i.e. higher frequencies as high notes and lower frequencies as low notes. If two tuning forks with frequencies of 256 hertz and 254 hertz are sounded simultaneously and at a certain instant an observer simultaneously receives a compression from each fork, the observer hears a loud sound. One quarter of a second later the 256 hertz tuning fork has gained one half of a vibration on the 254 hertz tuning fork so the observer simultaneously receives a compression from one tuning fork and a rarefaction from the other tuning fork. The compressions and rarefactions annul, or partly annul, each other and the observer hears minimum sound intensity. After another quarter second when one tuning fork has gained one vibration on the other, the observer again simultaneously receives two compressions and the sound is again of maximum intensity. So during the time interval in which one tuning fork gains one vibration on the other, the sound intensity passes through one cycle of change. i.e., one beat is heard. There will be two beats per second because the 256 hertz tuning fork makes two vibrations more than the 254 hertz tuning fork. If two sources of sound of frequencies f1 and f2 are simultaneously emitting sound waves, then the source of higher frequency, f1, gains one vibration on that of lower frequency (f1 - f2) times per second and an observer hears (f1 - f2) beats per second. The number of beats per second is equal to the difference between the frequencies of the two sources.
If two notes of slightly different frequencies are sounded together they interfere and periodically produce a loud sounding large amplitude called a beat. Beats are used by piano tuners to tune instruments. If two wave trains of frequencies 4 and 5 hertz are propagated so that each particle is subject to the joint action of the two waves, the displacement at any instant of any particle will be the algebraic sum of the separate displacements due to each wave. In the diagram, Curve 1. shows for a given particle the time displacement graph due to the wave train of frequency 5 hertz. Curve 2. is the time displacement graph for the wave train of frequency 4 hertz. The graphs are drawn in each case for an interval of two seconds. At an instant represented by the point A, the displacements, AB and AC, due to the two separate waves are both to the same side of the mean position of the particle and its resultant displacement at this instant is AD in Curve 3., equal to AB + AC. At the instant of time represented by the point E, the displacements due to the separate waves are to opposite sides of the mean position of the particle so the resultant displacement is EH = EF + (- EG). Curve 3. is the resultant time displacement curve for any particle. The resultant displacement is greatest when the displacement due to the waves assist each other. This waxing and waning of the resultant amplitude due to the superposition of two waves of like kind but of different frequencies and is called beats.

26.8.2 Interference of sound waves with tuning forks
Two sound waves of the same frequency and amplitude may give rise to easily observed interference effects at a point through which they both pass. If the crests of one wave fall on the crests of the other, the two waves are said to be in-phase. In that case, they reinforce each other and give rise to a high intensity at that point. However, if the crests of one wave fall on the troughs of the other, the two waves will exactly cancel each other. No sound will then be heard at the point. The two waves are then 180^o, or a half wavelength, out-of-phase. Intermediate effects are observed if the two waves are neither in phase nor 180^o out-of-phase, but have a fixed phase relationship somewhere in between. At the certain condition, two or more sound waves interact and combine to produce a resultant wave of larger or smaller amplitude.
Hold the handle of a tuning fork and knock it with a rubber hammer to start its vibration. Touch the rim of a table with the top of the tuning fork. Place the tuning fork upright near your ear. Gently rotate the tuning fork around a vertical axis for a circle (360^o). Take care of the change in volume. The vibration of the tuning fork generates the vibration of the table at the same frequency. They meet the condition of interference and form the interference field. Rotate the tuning fork to change the distribution of sound intensity. So you may hear the loudest sound 4 times and the lowest (nearly silent) sound 4 times. Silent zones can sometimes occur near a sound source, even when a sound can be heard further away. This happens when sound waves speed up and are refracted as they pass through warm air. The sound is deflected up and over a location causing a silent zone. If the sound then hits a belt of cold air as it rises then it will be refracted down again as it slows down.

26.8.3 Superposition of waves of equal frequencies with tuning forks
See diagram: 26.8.4.1
Hold a vibrating tuning fork near your ear and slowly rotate it about its shaft. Note the four positions in one revolution at which almost no sound is heard. See in the diagram the ends, A and B, of the prongs as viewed from above.
1. As the prongs approach each other, a compression forms at C and spreads out in the directions shown by the arrows from C. At the same time the rarefaction formed at R1 and R2 spread out as shown by the arrows from R1 and R2. So in the regions of the dotted lines a compression and a rarefaction arrive simultaneously and annul each other along these lines.
2. As the prongs move apart, a rarefaction forms at C and compressions form at R1 and R2. The rarefactions and compressions spread out to annul each other along the dotted lines.
3. So along the dotted lines the pressure re mains constant and these lines are lines of zero sound. The four positions of silence in one revolution of the fork correspond to the four dotted lines. The modifications of intensity obtained by superposing waves are called interference effects.

26.8.4 Superposition of waves of equal frequencies with loudspeakers
See diagram: 26.8.4.2
Mount two loudspeakers, A and B, near each other and operate them from the same source of high frequency, e.g. 3 000 cycles per second. The sound waves originating at each loudspeaker are superimposed in the region in front of them. At those points at which a compression from one loudspeaker arrives at the same instant as a rarefaction from the other loudspeaker, annulment occurs and the sound intensity is zero. At points where two compressions, or two rarefactions, arrive simultaneously, reinforcement results from the superposition of the two wave trains and these points are regions of maximum sound intensity. The thick and thin arcs represent the instantaneous positions of the zones of compression and rarefaction from A and B. At points marked x, annulment occurs and these points of zero sound intensity lie along lines radiating from between A and B. The points of intersection of two thick lines or of two thin ones are regions of maximum intensity. The existence of the above pattern in the region in front of A and B can be made evident by exploring the sound field with a microphone. It is found that alternating zones of maximum and zero sound as the microphone is moved across the sound field. You can use a sensitive flame to explore the interference pattern by keeping the flame in a fixed position and slowly rotate the sources of sound. The flame alternately dips and rises as the lines of maximum and zero intensity pass over it.

26.8.5 Wave interference in water, drop stones in water
Simultaneously drop two identical stones or marbles or golf balls into a calm pool of water. An interference pattern similar to the above occurs on the surface of the water. The ripples move out in circles. Where they cross each other note the brief patterns of constructive interference, two peaks at the same place at the same time (higher ripples) and destructive interference, a peak and a trough meet at the same time (lower ripples).

26.8.6 Loaded tuning fork
Use two tuning forks with the same frequency. Wrap a piece of sticking plaster around one prong of one tuning fork. Sound each tuning for separately. Note that the loaded tuning fork has reduced frequency. Sound the two tuning forks together. Note the throbbing sound due to the waxing and waning of the resultant amplitude.

26.8.7 Resonating objects have same frequency as source of vibration
Put two upright stands 50 cm apart and attach a string between them at the same height. Tie the short lengths of string to seven metal washers. Hang the washers on the horizontal string at the following hanging string lengths: washer l (20 cm), washer 2 (15 cm), washer 3 (20 cm)., washer 4 (15 cm), washer 5 (5 cm), washer 6 (10 cm). washer, washer 7 (5 cm). Start swinging washer 7 and observe the other washers. Washer 2 and washer 4 starts swinging with swing with washer 7. Repeat the experiment with washer 2 swinging first. Repeat the experiment with washer 1 swinging first. Washer 3 starts swinging with it. Washer 7 can be compared with the source of vibration and washer 2 and washer 4 have the same frequency of vibration. The same happens when washer 2 or washer 4 is started to swing first. The washers that have the same hanging string length will swing with the original swinging. The source of vibration can increase its own vibrations, e.g. when wind blows on it.

26.8.8 Energy transfer between pendulums by resonance
See diagram 4.2.2
Study how the time taken for energy transfer between pendulums depends on the following:
1. the distance between hanging points of the pendulums, and,
2. the length of the pendulums.
Suspend a 100 cm strong string between two stands. Attach two threads 2.5 cm each side of the centre of the strong string. Attach 100 g weights to the end of each thread so that the length of the thread is 50 cm. Pull one weight to the side through a 60^o angle to the vertical. While noting the time in seconds, release the weight so that it swings freely back and forth as a pendulum but does not touch the stationary second pendulum. The energy of the first pendulum transfers to the second pendulum. The first pendulum swings less until it stops swinging and the second pendulum swings more until it has the original swing of the first pendulum. Note the time when the first pendulum stops. The energy of the first pendulum transfers to the second pendulum. Note the time when the second pendulum stops. Note the times for five transformations of energy. Calculate the average time needed for one transformation of energy. Repeat the experiment by increasing the distance between the hanging points of the pendulums. Repeat the experiment by shortening the length of the thread.
Repeat the experiment by changing the initial angle of swing
Note how time of transfer depends on the following:
1. Distance between pendulums
2. Length of pendulums
3. Original angle of swing of pendulums
Note that the distance between pendulums affects the tension in the strong string.

Experiment	distance d	length l	angle a	Time 1 (sec.)	Time 2 (sec.)	Time 3 (sec.)	Time 4 (sec.)	Time 5 (sec.)	Total (sec.)	Average time (sec.)
1 (control)	2.5	50	60^o	.	.	.	.	.	.	.
2 (distance)	10	50	60^o	.	.	.	.	.	.	.
3 (length)	2.5	100	60^o	.	.	.	.	.	.	.
4 (angle)	2.5	50	30^o	.	.	.	.	.	.	.

26.9.0 Sound reproduction, loudspeakers, microphones, amplifiers, recorders, mechanical gramophone, electrical reproduction, photographic film, compact discs, lasers
Sound recording and reproduction, amplifier, transducer, microphone, loudspeaker, stethoscope, spiral seashell, sound track, sound gate, sound head, magnetic tape, stereophonic sound, sound level meter decibel (dB), music and noise, Dolby sound, noise pollution, waveform analysis. The 3 types of recording mechanisms are as follows: mechanical, magnetic and optical.

26.9.01 Transducer, carbon microphone in a telephone
A transducer converts a physical quantity (e.g. sound, light, heat), into an electric signal, or converts an electric signal into a physical quantity.. Transducers are used in microphones and loudspeakers (electroacoustic transducers), photocells and accelerometers. A recording head may consist of a magnetic, electric, mechanical or electro-optical transducer to record sound on magnetic tape, compact disc or film. A passive tranducer has only the incoming signal as its power source but and active transducer has an additional external power source for power gain.
A carbon microphone in a telephone has an aluminium diaphragm outside two carbon blocks in a mixture of carbon granules. The carton blocks connect to a power source and a receiver. Sound waves cause the diaphragm to vibrate that in turn causes the carbon blocks to move together or apart and change the current between the power source and the receiver.
In the receiver, the variable current from the microphone passes through the coils of an electromagnet that exerts variable magnetic force on an iron diaphragm to produce sound waves.

26.9.1 Direction of sound, microphone
Some microphones are directional and pick up sounds only coming from one direction. Set up a microphone and speakers in a room. Position the microphone at the front of the room with the speakers as far away from it as possible. Watch someone speaking into the microphone. Does the sound appear to be coming from this person or the speakers at the other end of the room? Next time you are watching a film at the cinema, try to find where the sound is coming from. Not all the speakers are located at the screen. Does the speech appear to originate from the people on screen or from the speakers located around the theatre? See if you can find where the speakers are and which sounds (speech or music) are emanating from which speakers. Listen to a stereophonic or quadraphonic sound system to experience surround sound. Next time you are in a noisy car try to find where the sounds come from.

26.9.2 Microphone and loudspeaker
See diagram 26.9.2 Loudspeaker
Wind the thick insulated copper wire around the dowel to make a coil 3 cm in diameter. Then wire up a circuit consisting of the battery, the rheostat and the copper coil. Glue the fridge magnet onto the cloth then hang it at one opening of the coil. Complete the circuit. Note how the magnet moves in response to the changing magnetic field that is produced in the coil as you change the setting on the rheostat. A loudspeaker works in exactly the same way as a microphone, but in reverse. An electric current from a microphone flows through the coil in the electromagnet that has a central pole and a surrounding ring pole. The force between the magnetic field of the coil and the magnet makes the coil vibrate in accordance with Fleming's left hand rule and the attached paper cone diaphragm vibrate to create sound waves as it pushes and pulls on the air next to it.

26.9.3 Record sound with a cassette recorder, compact disc and microphone
1. A cassette recorder consists of the protective plastic holder, the cassette, and two reels to allow the magnetic tape to pass from one reel to the other through an electromagnet recording head / reading head. Rewinding allows repeated use. Sound is recorded on the tape with magnetized particles of iron or chromium oxide. Electric current from a microphone that varies with a sound wave passes through a metal coil in the recording head that causes changes in e its magnetic field to rearrange the random pattern of the metal particles on the "blank" magnetic tape into a pattern that can be read by the playback head as a sound wave to be amplified by a loudspeaker.
Select a cassette container containing songs that you do not like. Unravel part of the magnetic tape from the recorder and pass a strong magnet over it. Play the cassette and the songs you do not like sound worse.
2. A compact disc, CD, stores sound as a binary code. represented by tiny pits or bumps etched into a layer of aluminium surrounded by flat areas called land. This is then coated with plastic for protection. When the laser beam is shone at the disc some of it is reflected back by the smooth aluminium land but not by the pits or bumps. Light reflected from the shiny underside land is read as binary 1. Light that hits the pit or bump is scattered and not reflected, so it is read as binary 0. The result is a series of digital pulses to be converted to sound by a loudspeaker. The laser itself does not touch the disc so it should not wear out. When the laser is tracking the speed of needle as it goes from the outside disc near the centre the disc spins at 500 revolutions per minute, towards the centre of the record. When it is tracking near the edge it spins at only 200 rpm so the same relative speed is maintained.
Let white light fall on the underside of a compact disc and note the diffraction caused by light passing through the gaps between the bumps.
3. Microphones contain a transducer to change one form of energy into another. This is actuated by sound waves. The microphone delivers electric signals proportional to the sound pressure. Sound hits a diaphragm made of paper or plastic and vibrates it. The vibrations are then converted into electric current.
Make some recordings of different people speaking. Recite a few ditties such as she sells seashells on the sea shore and Peter Piper picked a peck of pickled peppers. Play them back and listen to the quality of the sound. Listen for whistling and sound of breathing. Now try some different locations. Make a recording outside, make one in a hard reflecting room and one in a soft absorbing room. Find a windy place and make another recording. Again listen to the recorded sound. Watch a few interviews on television and take note of the different styles and types of microphones in use, e.g. "fluffy dogs" (large fluffy microphones used outside) and lapel "mikes" (microphones). Try to improve sound quality in your recordings. Recite at different distances from the microphone. Try drinking some water to stop sound of breathing and hissing sounds. Experiment by wrapping different types of cloth or sponge around the microphone to cut out other unwanted sounds.

26.9.3.1 Analogue recording and digital recording
In analogue transmission the characteristic of the transmission signal, e.g. amplitude or frequency, varies in direct proportion to the received sound or brightness of a picture. The hands of a clock is a form of analogue recording. In digital transmission the information is transmitted in a series of pulses thus eliminating unwanted noise. The pressure from a sound wave can be sampled many times in a second and the values recorded in numerical form using the binary code. The closer the sampling the the higher the fidelity of the sound recorded, i.e. more closely repeats the original sound. Later this information can be translated into the analogue form in the receiver. Digitally recorded information can be stored on a CD or sent through the internet.

29.9.4 Use a hand lens to examine the grooves in a vinyl disc gramophone record
1. A gramophone (US phonograph) reproduces sound using with a stylus or needle that vibrates by following a groove on a revolving spiral disc. The needle vibrates in the groove and vibrates a diaphragm. The sound produced this way is then made louder (amplified) by the horn on an old gramophone. The original stylus was like a thorn and could be kept sharp with a pencil sharpener. With repeated use the groove became worn causing loss of accuracy of the recorded sound and new sounds caused by dirt and dust. This is a mechanical recording method.
2. Poke a pin through the centre of the base of a polystyrene or cardboard cup. Set the record on a turntable and start the turntable spinning. Carefully hold the pin in the groove on the record and listen to the record at the opening of the cup. The sound recorded in the grooves is being picked up by the pin and then turned into vibrations and transmitted by the cup. Try the same activity with different sized cups. How does the size of the cup affect the sound produced?
3. Cut a point on one end of a match stick. Cut the other end into two, lengthwise, for about 1 / 4 the length if the match stick. Fit a piece of stiff paper into the split end. Hold the matchstick and paper point down onto an old 78 rpm phonograph records turning on a turntable. You can hear music coming from the paper. When you hold the match point in the grooves of the phonograph records the lateral vibrations from the grooves are transmitted to the paper. Vibration of the paper produces vibrations in the air that carry to your ear drum, so you hear the sound.

26.9.5 Glass tube with an open end, using signal generator
1. Connect the loudspeaker to the fan out [viz. outlet] of the signal generator with a piece of leader and place the loudspeaker at the open end of the glass tube. Turn on the signal generator and adjust it to the lowest frequency. The lower the frequency, the lower it sounds. Gradually increase its frequency slowly until the sound increases suddenly, here the air inside the tube resonates with the sound of the signal generator so that a standing wave forms at the lowest frequency inside the tube. The lowest frequency is called the fundamental, denoted as f₁. Measure the length of the glass tube, denoted as L. f1 may be expressed as, v = f₁w₁, where v is the velocity of travelling wave along the air column, i.e. the sound spreading velocity in the air, w₁ is wavelength, w₁= 4L. Gradually increase its frequency slowly again until the sound increases suddenly secondly. It shows that the air inside the tube and the frequency of forced vibration meet the condition of resonance again. The second standing wave forms, called harmonic wave, its wavelength, i.e. harmonic length denoted as L₁ and its frequency denoted as f₂. List the top 4 resonance frequencies. The sound velocity is a constant under that temperature and the glass tube has only one open end. So the frequency of the standing wave of the air column inside the glass tube is limited. At the closed end of the glass tube, the air molecules do not move, so. here must be the node of the standing wave. At the open end, the air pressure is always equal to the atmosphere pressure so here the air is not contracted, i.e. it has no change in shape. So the open end must be the antinode of the standing wave. When the air column emits the first standing wave, there are only one node and one antinode in the tube according to the vibration of the fundamental. When the air column emits the second standing wave, there are two nodes and two antinodes and the frequency of vibration is as 3 times as the fundamental. The vibration of the air column inside the tube with only 1 open end may just form the standing wave whose frequency is odd number times of the fundamental.
2. Glass tube with 2 open ends, using signal generator
Methods are the same as above. The 2 ends of the glass tube are all open so the two ends are all the antinodes of the standing wave. Corresponding to the vibration of the fundamental, there are 1 node and 2 antinodes in the tube, then 2 notes and 3 antinodes corresponding to the vibration of 2 times of the fundamental. Thus the vibration of the air column inside the tube with only 2 open ends may form the standing wave whose frequency is even number times of the fundamental.