1. J. Askill, Physics of Musical Sound, Van Nostrand: New York (1979).
2. M. J. Moravcsik, Musical Sound: An Introduction to the Physics of Music, Paragon House Publishers: New York (1987).
3. J. S. Rigden, Physics and the Sound of Music, John Wiley & Sons: New York (1977).
4. T. D. Rossing, The Science of Sound, Addison Wesley Publishing Company: New York (1982).
5. H. E. White and D. H. White, Physics and Music, Holt, Rinehart, & Winston: New York (1980).
6. A. Wood, The Physics of Music, John Wiley & Sons: New York (1975).
7. J. R. Pierce, The Science of Musical Sound, Scientific American Books, W. H. Freeman: New York (1983).
Most experiments involving sound are relatively safe except for the hazards not directly associated with the sound as discussed elsewhere. However, it is possible for very intense sounds to permanently damage the ear especially after prolonged exposure[1,2]. Consequently, in the demonstrations described here, the sound intensity should always be kept at a level well below the threshold of pain (see Table 3.1).
As a general rule, prolonged exposure to sound levels above 85 dB will cause slight hearing loss and above 90 dB will result in mild to moderate loss. Prolonged exposure to sound levels above 95 dB causes moderate to severe hearing loss. Above 100 dB, even short exposure can cause a permanent loss of hearing.
The ear has an acoustic reflex that protects the inner ear from loud sounds in the same way that the pupil of the eye protects the eye by contracting in the presence of bright lights. However, the reflex requires a few hundredths of a second to respond, and thus cannot be relied upon to protect the ear in the event of a short duration sound such as an explosion.
The damage is typically by way of tearing or ripping the microscopic hair cells of the cochlea. Such damage is usually only temporary unless the sound is frequent or sustained. Especially intense sounds are capable of rupturing the eardrum. The damage threshold is frequency-dependent, and the ear is most susceptible to damage by sounds of around 3000 Hertz in part because the auditory canal is a closed tube having a resonance in this region. Prolonged exposure to sounds of a particular range of frequencies can permanently reduce the sensitivity of the ear to those frequencies.
The monitoring of sound levels requires an A-scale sound level meter with a frequency response matched to the response of the ear or one capable of displaying the sound level for all of the various frequency ranges. Protection can be provided by ear plugs and/or ear muffs. Cotton in the ears is not an effective protection unless the cotton is wax-impregnated.
1. K. D. Kryter, W. D. Wood, J. D. Miller and D. H. Eldredge, Journ. Acoustical Soc. Am. 39, 451 (1966).
2. E. A. Lacy, Handbook of Electronic Safety Procedures, Prentice- Hall: Englewood Cliffs, New Jersey (1977).
3. A. P. G. Peterson and E. E. Gross, Jr., Handbook of Noise Measurement, General Radio: Concord, Massachusetts (1963).
Decibels Intensity Dp/po Example (dB) (W/m^2) 0 10^-12 2x10^-10 Threshold of hearing 20 10^-10 2x10^-9 Whisper (at 1 m) 40 10^-8 2x10^-8 Mosquito buzzing 60 10^-6 2x10^-7 Normal conversation 80 10^-4 2x10^-6 Busy traffic 100 10^-2 2x10^-5 Subway 120 1.0 2x10^-4 Threshold of pain 140 100 2x10^-3 Jet on carrier deck
The peculiar sound of one's voice after breathing helium or sulfur hexafluoride provides an amusing demonstration of the variation of the velocity of sound with the density of a gas.
A dramatic illustration of the variation of the speed of sound with the density of a gas is performed by breathing a low density and a high density gas and talking as the gas is expelled from the lungs. Suitable gases are helium and sulfur hexafluoride. Xenon, though more expensive, can be used in place of sulfur hexafluoride. The gases are most conveniently breathed by first filling a balloon from a gas cylinder with a pressure regulator set to about 5-10 psi. One should exhale the air from the lungs and then inhale the gas through the mouth as if sucking a straw. The gas is then slowly exhaled as one talks. A duck hat for the helium and a cowboy had for the sulfur hexafluoride adds to the humor.
One can also fill a balloon with sulfur hexafluoride and tie it off. It is distinctly heavier than an equivalent air balloon as can be illustrated by dropping the two side by side.
An especially instructive demonstration is to breathe a mixture of helium and sulfur hexafluoride in a proportion such that its density is close to the density of air. This can be done by first filling the balloon with helium and then adding just enough sulfur hexafluoride so that the balloon is slightly heavier than air (like an air-filled balloon). In principle, one's voice should sound normal after breathing such a mixture, but in practice the helium rises first into the nasal cavity and is expelled, leaving the sulfur hexafluoride which is exhausted at a slower rate. Such a demonstration shows that the density of the gas rather than its particular composition is the relevant variable.
The speed of sound in a gas is proportional to the square root of its density. For helium the speed is 2.7 times the speed of sound in air. For sulfur hexafluoride the speed is 0.44 times the speed of sound in air. The speed of sound in air is 343 m/s or 750 mi/hr at 20°C and is proportional to the square root of the absolute temperature.
The voice sounds different because the natural resonant frequencies of cavities in the head are raised or lowered in proportion to the speed of sound. Of course the resonant frequencies of these cavities are only one ingredient in the way we sound. The gas does not alter the frequency of the vocal cords nor does it affect how fast we talk. The vocal tract acts as a filter for the sounds produced by the vocal cords in a manner similar to the treble and bass controls on a stereo.
Most people have heard the distinctive yet highly amusing sound that results when one breathes helium. Deep sea divers often breathe an atmosphere that is largely helium so that they can exist in a high pressure environment without exceeding the body's tolerance for nitrogen and oxygen. Most people have not heard the equally amusing sound that results from breathing sulfur hexafluoride. Sulfur hexafluoride has the additional property that, since it is a high density gas, it tends to remain in the lungs for a long time, and thus the effect on the voice persists much longer.
The major danger in performing this demonstration is hypoxia from not getting enough oxygen while the gas is being breathed. Thus one should not immediately repeat the demonstration but wait a minute or so before breathing more gas. It is a good idea to take a few deep breaths before and after each demonstration. One should point out to the audience that the breathing of most gases (even some air) is potentially harmful. Helium and sulfur hexafluoride are two of a very small number of gases with which this demonstration can be safely done. The substitution of other gases, especially flammable gases such as hydrogen, is not recommended.
1. A. H. Cromer, Physics for the Life Sciences, McGraw Hill: New York (1977).
An oscilloscope is used to display the waveforms of various musical instruments in order to show the effect of frequency and wave shape on the sound.
Sine waves can be produced with tuning forks or organ pipes or with an electronic function generator. One could first show the sounds corresponding to sine waves of different frequencies. Anyone in the audience with perfect pitch should be able to identify the musical notes (see Table 3.2). The way in which musical scales are constructed makes an interesting digression[1,2]. The standard of A-440 is not universally accepted, nor is the even-tempered scale. Some scientific manufacturers once adopted a standard of 256 (28) for middle C, but musicians ignored it. With a function generator, one can show the frequency limits of hearing (approximately 20 Hz to 20 kHz).
Musical instruments such as a violin and a trumpet have distinctive waveforms[3,4]. The clarinet somewhat resembles a square wave. One could show examples of string, wind, and percussion instruments. One can illustrate frequency modulation (vibrato) and amplitude modulation (tremolo). If someone in the audience can play the instruments, it adds a touch of interest to have them do so. Alternately, an accomplished musician can be planted in the audience who when called upon pretends minimal skills until suddenly launching into "The Flight of the Bumblebee" or some similarly intricate piece.
Modern electronic keyboards can be used to emulate a wide variety of musical instruments. Demonstrating the difference in waveform between a real instrument and a synthesized instrument can be quite interesting. The complex waveform required to transmit speech and music is especially dramatic.
Square waves and other waveforms can be produced with a function generator connected to an amplifier and speaker as well as to an oscilloscope. One could illustrate the different sounds produced by sine waves and square waves of the same frequency. The difference results from what musicians call "overtones" and physicists call "harmonics." Harmonics are integral multiples of the fundamental frequency, but overtones may or may not be related to the fundamental in a simple way. In most string and wind instruments, the overtones form a harmonic series, but in percussion instruments such as the drum, the overtones are more complicated and less "harmonious" (not a single discernible note). The combination of overtones is what gives each musical instrument its characteristic quality, or timbre.
This demonstration offers the opportunity to exhibit unusual musical instruments and other sources of sound. One might try blowing over the top of a soft-drink bottle and alternately drinking from it to change its pitch. The same can be done with a flexible plastic tube (1/2" diameter Eastman Poly-Flo) partially filled with colored water, fruit juice or wine, which one can drink when done. The bottom can be cut out of a Coke bottle, and different notes played by blowing over the top while it is dipped different depths into a beaker of water. Wine glasses stuck with a small mallet or rubbed along the rim with a clean, grease-free finger emit good sine waves. Music has been written for such a glass harmonica. A bent saw blade, whistles, horns and sirens are other possibilities. A long, hollow pipe, open on both ends, lowered over a Bunsen burner can also be made to emit a sound, as was first done by Sir Charles Wheatstone (1802-1875) in a series of public lectures at the Royal Institution in London.
An especially impressive demonstration can be done with an aluminum rod about a centimeter in diameter and at least a meter long. Hold the rod at the center in one hand. Put powdered resin on the fingers of the other hand and stroke the rod along its length to excite longitudinal vibrations. These vibrations have a high pitch and vibrate for a very long time after one stops stroking. Thus they are extremely sinusoidal. The sound can be stopped abruptly by touching one of the antinodes at either end of the rod. Then grip the rod at a point one quarter of the length from one end and repeat the stroking to excite the second harmonic. It helps to place a mark at the right spot.One can compare these longitudinal vibrations with the transverse vibrations that occur when the rod is struck with a mallet. The transverse vibrations are at a much lower frequency unless the rod is very short as in a xylophone.
One can illustrate that the perceived loudness of a sound depends upon its wave shape. The square wave sounds louder than a sine wave of the same frequency because of the harmonics, even when the amplitude of the square wave is lowered by (pi/2)½ to account for its larger average power. Also the perceived pitch of a sound depends slightly on its intensity. Usually the pitch change is downward at low frequencies and upwards at high frequencies as the loudness increases, but the effect varies considerably with the individual. Furthermore, the effect is noticeable only for sine waves[9,10]. These perceptions can be demonstrated with a pair of function generators and a switch to alternate between the two. If the sources are sounded simultaneously, the presence of beats can obscure the effect.
An inexpensive transistor radio can be connected to the oscilloscope to illustrate the distortion that results when the volume is turned up too high and the waves are flattened due to saturation of the transistor amplifiers. This could lead to a discussion of high fidelity audio equipment and the need for high power amplifiers to minimize distortion due to the generation of harmonics.
By tuning a radio or television between stations, one can demonstrate what noise sounds like. There are many types of noise such as white noise (all frequencies present in equal amounts), 1/f noise (sometimes called pink noise), 1/f2 noise (sometimes called brown noise since it is characteristic of brownian motion), and others. Commercial noise generators are available that produce the various types. Alternately various kinds of noise can be simulated by filtering white noise through an audio equalizer (adjusted to unequalize).
It is interesting to note that the shape of a waveform is determined by its Fourier frequency components. The phase as well as the amplitude of the individual frequency components will affect the shape of the waveform, but since the ear is insensitive to the relative phases of the components of a wave, waveforms of quite different shapes may sound identical to the ear.
There are no precautions other than keeping the sound intensity down to a safe level.
1. J. Backus, The Acoustical Foundations of Music, W. W. Norton & Company: New York (1969).
2. E. E. Helm, Scientific American 217, 93 (Dec 1967).
3. H. Lineback, Scientific American 184, 52 (May 1951).
4. C. A. Culver, Musical Acoustics, McGraw-Hill: New York (1956).
5. J. S. Miller, Am. Journ. Phys. 27, 367 (1959).
6. J. Tyndall, Sound, third edition, Longman: London (1975).
7. S. S. Stevens, Journ. Acoustical Soc. Am. 6, 150 (1935).
8. A. Cohen, Journ. Acoustical Soc. Am. 33, 1363 (1961).
9. W. B. Snow, Journ. Acoustical Soc. Am. 8, 14 (1936).
10. D. Lewis and M. Cowan, Journ. Acoustical Soc. Am. 8, 20 (1936).
11. G. von Bekesy, Experiments in Hearing, McGraw-Hill: New York (1960).
Note Frequency C 261.63 Hz C# 277.18 Hz D 293.66 Hz D# 311.13 Hz E 329.63 Hz F 349.23 Hz F# 369.99 Hz G 392.00 Hz G# 415.30 Hz A 440.00 Hz A# 466.16 Hz B 493.88 Hz C 523.25 HzaA-440 is used as the standard, and the interval between each note is 21/12 = 1.05946.
A reed mounted on the end of a rotating arm produces a tone whose pitch wobbles up and down as the arm rotates.
The Doppler effect (named after the Austrian, Christian Johann Doppler, 1803-1853) can be illustrated in a device which consists of a reed mounted on the end of an arm that is spun by means of a motor with suitable gears to control the speed. The rotation causes air to pass over the reed producing a sound whose pitch wobbles up and down as the reed successively moves toward and then away from the observer. It helps if the speed of rotation can be adjusted. If a microphone is being used, it should be turned off or placed on the side of the apparatus toward the audience to reduce the interference between the direct and amplified sounds. The spinning arm can be viewed with a strobe lamp to freeze its motion. Alternate techniques for exhibiting the Doppler effect are also available[2-4]. A smoke detector wired so as to emit a continuous tone can be swung around on the end of a rope.
One can illustrate the effect verbally, but a tape recording of a train whistle or a car horn is more effective. Recordings of the Doppler effect can often be found on sound effect albums at record libraries or made quite easily with a tape recorder and automobile on a country road. This makes a good weekend family project for students who can then share their results with their classmates.
The frequency heard by a fixed observer for a source in motion is given by f = fov/(v ± vs), where fo is the frequency of the source, vs is its velocity and v is the velocity of sound (about 343 m/s in air at 20°C). The plus sign holds for motion away from the observer, and the minus sign holds for motion toward the observer. Thus if one wants to produce a ±5% frequency shift for a reed at the end of a 25-cm-long arm, a rotation speed of about 650 rpm is required.
The Doppler effect was tested by a rather bizarre experiment in Holland a few years after Doppler derived his formula in 1842. For two days a locomotive pulled a flat car back and forth at different speeds. On the flat car were trumpeters sounding a particular note. On the ground, musicians with a sense of absolute pitch recorded the note as the train approached and receded.
There are many examples in nature of the Doppler effect. In addition to the usual train whistle and car horn, the Doppler effect also occurs for electromagnetic waves, but since the velocity of light is much larger than the velocity of sound, the effect is much smaller for a given source velocity. Even so, the police use Doppler radar to catch speeders. Doppler radar is now used to measure the speed of baseballs and tennis balls. In air traffic control, the Doppler effect is used to discriminate against stationary targets and to detect wind shear. The Doppler effect is also important in the reception of radio signals from earth-orbiting satellites. The Doppler effect is used in the determination of the distance of galaxies[5,6] (the Hubble constant) and in the Möessbauer effect.
The main hazard in this demonstration is coming in contact with the rapidly rotating arm. A switch and speed control should be provided that permits operation from a safe distance. The apparatus should not contain parts that could come loose and be thrown out into the audience.
1. H. A. Robinson, ed., Lecture Demonstrations in Physics, American Institute of Physics: New York (1963).
2. F. S. Crawford, Am. Journ. Phys. 41, 727 (1973).
3. H. F. Meiners, Physics Demonstration Experiments, Vol I, The Ronald Press Company: New York (1970).
4. J. S. Miller, Physics Fun and Demonstrations, Central Scientific Company (1974).
5. E. Hubble, Proc. Natl. Acad. Sci. 15, 168 (1929).
6. E. Hubble and M. Humason, Astrophys. J. 74, 43 (1931).
An electric bell in a jar makes a sound that decreases in intensity as the air is evacuated from the jar.
The necessity of a medium for the propagation of sound can be demonstrated by means of an electric bell (a doorbell type) in an evacuated bell jar. The electrical leads for the bell can be brought out of the bell jar through vacuum feedthroughs. Transmission of sound by the electrical leads can be kept to a minimum if they have a small cross-section and are rather long and coiled up. They can be led through a rubber stopper in a hole in the glass to further dampen the transmitted sound. The bell should be suspended by its leads so as not to touch the bell jar. The bell is turned on, and the bell jar is evacuated to a pressure in the millitorr range with a mechanical pump while the sound slowly diminishes until it is almost inaudible. With a sound meter and pressure gauge, one could plot the sound intensity as a function of pressure.
In a simpler version, a small bell with a clapper is mounted inside a jar small enough to be held in the hand and shaken. The jar is equipped with a rubber stopper, hose and shut-off valve.
The sound propagation should cease when the mean free path for air molecules becomes longer than a few centimeters. At room temperature and 760 torr of pressure (1 atmosphere), the mean free path is about 2 x 10-5 cm and is inversely proportional to pressure. Thus the pressure should ideally be reduced to about 10 millitorr to reduce the sound to the lowest possible level.
The only significant hazard with this demonstration is implosion of the bell jar. If the jar is designed for vacuum use (heavy flint glass), it should be safe so long as it is not struck with a heavy object or otherwise cracked. The bell should be of the type that operates from a low voltage (0-6 volts) so as not to pose an electrical hazard. A variation of the demonstration, in which one places a battery inside the bell jar to operate the bell, is not recommended since the battery may explode when exposed suddenly to a vacuum.
The difference in wave propagation speed for transverse waves on ropes of different masses and tensions is illustrated with a stick and two, 3x5-inch index cards.
One end of a rope is attached to the wall at about eye level. The rope is stretched across the room, and the free end is given a flick with the wrist. One can show that the speed of the wave on the rope increases with the tension in the rope but is independent of the shape of the wave. Dispersion (change in the shape of the wave as it propagates) can be observed. The reflection of the wave at the fixed end can be discussed. Note that the wave is inverted upon reflection from the fixed end.
Two identical ropes are strung across the front of the lecture room. The tension is made different by placing one end of each rope over a pulley and hanging different weights on each with the other end of the ropes anchored securely in the opposite wall. Two, 3x5-inch index cards (preferably different colors) are folded and placed one over each rope about a foot from the anchored end. The opposite ends of the ropes are then struck simultaneously with a stick while the audience is told to watch the cards. The card over the rope with the greatest tension will jump off the rope slightly, but very noticeably, before the other.
To illustrate the variation of velocity with mass density, two ropes are used, with obviously different masses (say a quarter-inch-diameter and a half-inch-diameter rope). For ropes of the same material, the mass per unit length is proportional to the square of the diameter of the rope. The ropes are attached together and passed around a single pulley so as to produce the same tension in each. Cards are placed over the ropes near the ends that are anchored separately to the wall, and the ends that are passed around the pulley are struck with a stick as described above. The card over the smaller rope will jump off before the other.
One can combine the two demonstrations by using two ropes with different mass densities under different tensions, but with the same ratio of tension to mass density. In such a case, the cards should jump off simultaneously.
The ropes should be strung across the room above head level to prevent walking into them. Care should be exercised to ensure that the weights do not fall on a foot if a rope breaks, comes loose from its anchor in the wall or slips off its pulley.
Two sound sources of nearly equal frequencies and amplitudes are made to exhibit beats if the frequency difference is less than about 10 Hertz.
The beating of two identical organ pipes can be used to illustrate the variation of the velocity of sound with temperature. Two identical glass tubes are placed one in each organ pipe, and the pipes are tuned for zero beating. A nichrome wire is lowered into one of the glass tubes and heated to 250-300°C by an ac current. A noticeable beating should occur as the resonant frequency of the heated pipe rises with the increased velocity of the sound. The wire can then be cooled until the beats disappear.
The explanation of the beating can be presented graphically by drawing two sine waves of slightly different frequencies on the blackboard and showing how they constructively interfere at certain times and destructively interfere at others. For an audience versed in trigonometry, a single trigonometric identity yields the result: sin(w1t) + sin(w2t) = 2sin[(w1+w2)t/2]cos[(w1-w2)t/2]. Thus two sounds of frequency w1 and w2 will be perceived as a single frequency (w1+w2)/2 but with an intensity that reaches a maximum twice during each cycle of the frequency (w1-w2)/2. Thus the beat frequency is w1- w2 (assuming w1 is the larger frequency). If the two sounds are of unequal amplitude, the cancellation will not be perfect when the waves destructively interfere, and the intensity variation of the beat will be less pronounced. Note that there is no wave present at the beat frequency. This can be illustrated by using two frequencies above the audible range of hearing but adjusted so that the beat frequency is within the audible range. Actually, if the sounds are sufficiently intense, it is sometimes possible to hear the beat frequency of two inaudible sounds because of nonlinearities in the ear.
Beats provide a means for musicians and piano tuners to tune their instruments. The tension in a violin string is adjusted until a given note gives a zero beat frequency with a standard note being played by the concert master. Other notes can then be adjusted so that their overtones beat with the overtones of the standard. In fact, the just diatonic scale is arranged so that the different notes are related in frequency by the ratios of small integers so as to minimize the beating of the overtones when two notes are played together. Such a scale seems to give the most pleasing sound, although instruments are more typically tuned to the even tempered scale in which the notes have twelve even logarithmic intervals within each octave and thus produce some low frequency beating among their harmonics.
Beats appear to play an important role in our perception of the quality of music. A low frequency beat (a few Hertz or less) can sound pleasing, in that it emulates the trembling of the human voice. Rapid beats can be very unpleasant to the ear just as a flickering light is unpleasant to the eye and a fingernail scratched across a surface is unpleasant to the touch. Thus when one singer in a chorus or one instrument in an orchestra is off key, the resulting beats render the sound highly obnoxious. The famous german physicist and acoustician (and chronically bad lecturer), Hermann von Helmholtz (1821-1894), had a reed organ built that was based on a 24 note scale optimized to reduce the beating between the harmonics of the various notes. The sound was reported to be very pleasing but apparently not sufficiently so to revolutionize the way in which music is written and played.
There are no precautions other than keeping the sound intensity down to a safe level.
1. H. A. Robinson, ed., Lecture Demonstrations in Physics, American Institute of Physics: New York (1963).
2. R. E. Miers and W. D. C. Moebs, Am. Journ. Phys. 42, 603 (1974).
3. S. H. Vegors, Jr., Am. Journ. Phys. 43, 1103 (1975).
4. H. F. Meiners, Physics Demonstration Experiments, Vol I, The Ronald Press Company: New York (1970).
5. H. L. F. Helmholtz, On the Sensations of Tone as a Physiological Basis for the Theory of Music, Dover: New York (1954).
A glass beaker exposed to a sufficiently intense sound wave at its natural resonant frequency is made to shatter.
In this classic demonstration[1,2] the input of the audio amplifier is connected to the variable-frequency, sine wave generator, and the output is connected to the loudspeaker. The glass beaker is set on some material such as a styrofoam pad that allows it to ring with minimal damping and is placed a few inches from the speaker. The beaker is tapped near its open mouth with a small mallet to ensure that it rings with a slowly decaying tone. With a microphone and oscilloscope, the resonant frequency can be measured and shown to the audience. Alternately, the speaker can be connected directly to the input of the oscilloscope and used as a microphone. The sine wave generator must be tuned to exactly the same frequency as the natural resonant frequency of the beaker.
Without an oscilloscope, one can adjust the frequencies to be equal by repeatedly tapping the beaker with the mallet and listening for the beats with the sound from the speaker as the generator frequency is slowly varied. This works best if the sound level is about the same from the speaker and from the beaker. Alternately, one can put the speaker near the beaker at a low sound level and listen for the increase in sound intensity as the resonant frequency is approached. Still another method is to watch or feel the vibrations of the beaker with the fingertips as the frequency is varied. Strips of paper folded over the edge of the beaker give an indication of the amplitude of the vibration. It is best to find the proper frequency beforehand using a digital frequency meter and to record the value (to a precision of at least one Hertz). This is so that the resonance condition can be quickly found for the demonstration, although there is considerable pedagogic value in showing how the resonance is found if time permits.
The members of the audience are then cautioned to cover their ears, and the sound is turned up to a high level. A slight readjusting of the frequency may be required. The frequency must be adjusted very slowly, and one must wait a few seconds for the oscillations to build to a value sufficient for the glass to break.
The demonstration can also be done with a wine goblet or any other glassware with vertical sides that exhibits a high quality resonance in the acoustical range. All that is required to test the quality of the resonance is to tap the glass with a fingernail or a pencil and listen to how long the resulting ringing lasts. Any glassware that can be made to ring for more than a few seconds should suffice. Glass with a high lead content works best. In a variation of the demonstration, one can use a fixed frequency sound source, tuned slightly below the natural resonant frequency of the glass, and then slowly add water or other liquid to the glass until its resonant frequency is lowered to match that of the sound source.
A strobe lamp tuned near the resonant frequency of the beaker or one of its harmonics allows one to observe the vibrations of the glass, although visibility is difficult except for those relatively close. A television camera and monitor can be used to improve visibility. Prior to breaking, the glass may deflect by as much as a centimeter.
This demonstration illustrates that a sound wave is a compressional wave with a characteristic frequency. The wave carries significant energy from the source to the point where it is absorbed.
More importantly, the demonstration illustrates the phenomenon of resonance. The Q (quality) of the resonance is defined as 2(pi) times the number of cycles (number of radians) required for the energy of an oscillation to decay to 1/e (37%) of its initial value. Thus the highest Q resonance is the one for which the ringing lasts the longest. A piece of glassware with a resonance at 1000 Hz that decays to 37% of its initial energy in one second has a Q of about 6000. The Q is also a measure the amplitude which an oscillator driven at its resonant frequency will acquire. Thus the glass with a Q of 6000 will vibrate with about 6000 times more energy when driven at resonance than when driven well off resonance with a sound of the same intensity. However, it takes about Q radians (one second in this example) for the oscillation to build to near its full amplitude. The driving frequency also has to be matched to the natural frequency to a precision of about 1/Q (one part in 6000 in this example). Since the sound intensity has to be high (in excess of 90 dB), precisely of the right frequency, and sustained for a few seconds, there is little danger of breaking one's wine glass while casually listening to music on the stereo!
Dorothy Caruso denies rumors that her husband Gigli could shatter wine glasses with his unamplified voice. Although it might be possible for a singer to do so, there are no documentated cases of any having succeeded. The Memtek company in Forth Worth, Texas produced a television commercial showing Ella Fitzgerald and others breaking glasses with recordings of their voices on Memorex tape.
1. W. Walker, Phys. Teach. 15, 294 (1977).
2. H. Kruglak, R. Hiltbrand and D. Kangas, Phys. Teach. 28, 418 (1990).
3. H. Kruglak, Phys. Teach. 17, 49 (1979).
A pipe several meters long filled with natural gas and connected to a loudspeaker produces a flame whose intensity varies with position along the length of the pipe.
A brass or copper pipe about 5 cm in diameter and 2 meters long contains several hundred small-diameter holes in a line along the length of the pipe. A downspout pipe will also work. One end of the pipe is sealed and fitted with a nozzle through which natural gas, methane or propane can be admitted. On the other end of the pipe is mounted a loudspeaker so as to make a reasonably tight seal. The loudspeaker is connected to the output of an audio amplifier whose input is connected to a sine wave generator of variable frequency.
The gas is turned on, and after waiting a few seconds for the air to be expelled from the pipe, the gas is ignited with a match where it exits the holes along the pipe. This produces a nearly continuous wall of flame several meters long. A considerable throughput of gas is desired, and the effect is best when viewed in subdued illumination. The frequency and amplitude of the sound emitted by the speaker is adjusted until a clear standing wave pattern is seen in the flame. At certain frequencies, the wave will resonate in the pipe, and the required amplitude will be quite small. More amplitude is usually required as the frequency is increased, but one should be careful not to burn out the speaker. As the frequency is raised, the distance between adjacent wave crests will decrease. The demonstration can also be done with other wave shapes such as square waves or the waves corresponding to speech and music.
The fundamental principle illustrated in this demonstration is the compressional wave nature of sound. Where the average pressure is greatest, the gas emitted through the holes is greatest, and the flame is most intense. The flame intensity is low where the wave displacement is maximum as a result of the Bernoulli effect. The information resembles that displayed on an oscilloscope but is more direct and less mysterious.
The variation of wavelength with frequency (or pitch) of the sound is easily illustrated. With a meter stick one can show that the product of frequency and wavelength is a constant equal to the velocity of sound (about 460 m/s in methane at 20°C). Note that the distance between the nodes of the flame is half a wavelength.
This demonstration also illustrates the resonant frequencies of a closed organ pipe. The closed end of the pipe is a displacement node (the air cannot move there) and thus is a pressure antinode (maximum) since the displacement and the pressure are 90° out of phase with one another. Conversely, the end driven by the speaker is a displacement antinode and a pressure node.
A resonance will occur in the pipe when the length of the pipe is an odd multiple of a quarter wavelength. At resonance the pressure variation within the pipe becomes quite large, and a relatively low sound intensity results in a large variation in flame intensity. As the pipe heats up, the sound velocity changes (proportional to the square root of the temperature in Kelvins) and a slight readjustment of the frequency is required to maintain resonance. Variation in the air-to-gas ratio also causes the resonance to drift.
The flame should be placed well away from any materials that it might ignite. The pipe becomes quite hot after prolonged operation and requires some time to cool off. If the flame is lit too quickly after the gas is turned on while there is still air in the pipe, the flame could be sucked into the pipe, destroying the speaker. The substitution of other flammable gases such as ethane or hydrogen is not recommended.
Various sources of sound with frequencies above the range of audibility are used to illustrate the distinction between a physical sound wave and the perception of sound.
**Available from Carolina Biological Supply Company, Cole Parmer Instrument Company, Edmund Scientific and Sargent-Welch Scientific Company
This demonstration can be introduced with the old question of whether a tree falling in a deserted forest makes a sound. The answer depends upon whether sound is defined as a physical wave or the perception of that wave by the ear and brain of a living creature. Sources of ultrasound provide a means to produce a sound wave that is not perceived by humans as being a sound.
Probably the least expensive and most convenient source of ultrasound is a dog whistle. A dog trained to come to the sound of the whistle who interrupts the presentation when it is first demonstrated will get the attention of the audience. Such whistles can usually be adjusted from a frequency that is barely audible to most people to well above the range of hearing. Ultrasonic pest repellers are sold that emit a very intense burst of ultrasound every few minutes.
A variable-frequency audio oscillator with a high-fidelity audio amplifier and good quality speaker (tweeter preferred) can be used to explore the whole range of audible frequencies. One can point out that high frequency audible response deteriorates with age (a condition known as "presbycusis"). If the audience consists of many ages, one could perform an experiment on this. One reason that children and small animals are more responsive to high frequencies is a simple matter of size scaling. An ear with smaller components is more sensitive to the shorter wavelengths of a high-frequency sound.
An oscilloscope with microphone can be used to prove that there is a sound present. Most microphones have low sensitivity to ultrasonic frequencies, but with a sensitive oscilloscope they can usually be made to indicate the presence of a sound. A high-pass filter between the microphone and oscilloscope is of considerable help. A small capacitor will often suffice. Ultrasonic microphones can also be purchased.
Another common source of sound above the audible range is an ultrasonic cleaner which usually consists of a vat of liquid with an ultrasonic transducer that creates sound waves in the liquid. Typically the liquid is some organic compound capable of dissolving oil and grease. Jewelers often use ultrasonic cleaners to clean rings and other jewelry. A freshly opened plastic bottle of carbonated beverage partially emersed in the liquid can be made to erupt and spray its contents several feet into the air.
Because of the short wavelengths, ultrasonic transmitters and receivers are well suited for the display of interference and diffraction effects usually demonstrated with microwaves or light. This helps to dispel the mystery of why, if light and sound are both waves, we can hear around a corner but we cannot see around one.
A sound wave is a compressional disturbance that will propagate in most materials. The range of human hearing is usually taken to be about 20 Hz to 20 kHz, although it is more accurate to say that the ear is most sensitive to frequencies around 4000 Hz and becomes progressively less sensitive at higher and lower frequencies requiring greater sound intensity to produce a detectable response. The product of the frequency and the wavelength is equal to the speed of sound in the medium. In air at 20°C, the speed of sound is 343 m/s, and so the corresponding wavelengths are 17.15 meters to 1.715 cm, respectively. Typical ultrasonic sources produce frequencies from about 20 to 100 kHz, corresponding to wavelengths as short as a few millimeters.
The reason it is difficult both to produce and to detect ultrasound is that something has to move to create or to respond to the sound wave. The inertia of the object (eardrum or whatever) prevents it from moving appreciably during the short period of the wave. Even so, the human ear is a remarkable instrument, responding to displacements of the ear drum that are hardly larger than the diameter of an atom!
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J. C. Sprott