CONCEPT
The area of physics known as acoustics is devoted to the study of the production, transmission, and reception of sound. Thus, wherever sound is produced and transmitted, it will have an effect somewhere, even if there is no one present to hear it. The medium of sound transmission is an all-important, key factor. Among the areas addressed within the realm of acoustics are the production of sounds by the human voice and various instruments, as well as the reception of sound waves by the human ear.
HOW IT WORKS
Wave Motion and Sound waves
Sound waves are an example of a larger phenomenon known as wave motion, and wave motion is, in turn, a subset of harmonic motion—that is, repeated movement of a particle about a position of equilibrium, or balance. In the case of sound, the “particle” is not an item of matter, but of energy, and wave motion is a type of harmonic movement that carries energy from one place to another without actually moving any matter.
Particles in waves experience oscillation, harmonic motion in one or more dimensions. Oscillation itself involves little movement, though some particles do move short distances as they interact with other particles. Primarily, however, it involves only movement in place. The waves themselves, on the other hand, move across space, ending up in a position different from the one in which they started.
A transverse wave forms a regular up-and-down pattern in which the oscillation is perpendicular to the direction the wave is moving. This is a fairly easy type of wave to visualize: imagine a curve moving up and down along a straight line. Sound waves, on the other hand, are longitudinal waves, in which oscillation occurs in the same direction as the wave itself.
These oscillations are really just fluctuations in pressure. As a sound wave moves through a medium such as air, these changes in pressure cause the medium to experience alternations of density and rarefaction (a decrease in density). This, in turn, produces vibrations in the human ear or in any other object that receives the sound waves.
Properties of Sound Waves
cycle and period. The term cycle has a definition that varies slightly, depending on whether the type of motion being discussed is oscillation, the movement of transverse waves, or the motion of a longitudinal sound wave. In the latter case, a cycle is defined as a single complete vibration.
A period (represented by the symbol T) is the amount of time required to complete one full cycle. The period of a sound wave can be mathematically related to several other aspects of wave motion, including wave speed, frequency, and wavelength.
The speed of sound in various media
People often refer to the “speed of sound” as though this were a fixed value like the speed of light, but, in fact, the speed of sound is a function of the medium through which it travels. What people ordinarily mean by the “speed of sound” is the speed of sound through air at a specific temperature. For sound
Because the sound generated by a jet engine can damage a person’s hearing, airport ground crews always wear protective headgear.
traveling at sea level, the speed at 32°F (0°C) is 740 MPH (331 m/s), and at 68°F (20°C), it is 767 MPH (343 m/s).
In the essay on aerodynamics, the speed of sound for aircraft was given at 660 MPH (451 m/s). This is much less than the figures given above for the speed of sound through air at sea level, because obviously, aircraft are not flying at sea level, but well above it, and the air through which they pass is well below freezing temperature.
The speed of sound through a gas is proportional to the square root of the pressure divided by the density. According to Gay-Lussac’s law, pressure is directly related to temperature, meaning that the lower the pressure, the lower the temperature—and vice versa. At high altitudes, the temperature is low, and, therefore, so is the pressure; and, due to the relatively small gravitational pull that Earth exerts on the air at that height, the density is also low. Hence, the speed of sound is also low.
It follows that the higher the pressure of the material, and the greater the density, the faster sound travels through it: thus sound travels faster through a liquid than through a gas. This might seem a bit surprising: at first glance, it would seem that sound travels fastest through air, but only because we are just more accustomed to hearing sounds that travel through that medium. The speed of sound in water varies from about 3,244 MPH (1,450 m/s) to about 3,355 MPH (1500 m/s). Sound travels even faster through a solid—typically about 11,185 MPH (5,000 m/s)—than it does through a liquid.
Frequency
Frequency (abbreviated f) is the number of waves passing through a given point during the interval of one second. It is measured in Hertz (Hz), named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894) and a Hertz is equal to one cycle of oscillation per second. Higher frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per second) or megahertz (MHz; 106 or 1 million cycles per second.)
The human ear is capable of hearing sounds from 20 to approximately 20,000 Hz—a relatively small range for a mammal, considering that bats, whales, and dolphins can hear sounds at a frequency up to 150 kHz. Human speech is in the range of about 1 kHz, and the 88 keys on a piano vary in frequency from 27 Hz to 4,186 Hz. Each note has its own frequency, with middle C (the “white key” in the very middle of a piano keyboard) at 264 Hz. The quality of harmony or dissonance when two notes are played together is a
Piano strings generate sound as they are set into vibration by the hammers. The hammers, in turn, are attached to the black-and-white keys on the outside of the piano.
function of the relationship between the frequencies of the two.
Frequencies below the range of human audibility are called infrasound, and those above it are referred to as ultrasound. There are a number of practical applications for ultrasonic technology in medicine, navigation, and other fields.
Wavelength
Wavelength (represented by the symbol X, the Greek letter lambda) is the distance between a crest and the adjacent crest, or a trough and an adjacent trough, of a wave. The higher the frequency, the shorter the wavelength, and vice versa. Thus, a frequency of 20 Hz, at the bottom end of human audibility, has a very large wavelength: 56 ft (17 m). The top end frequency of 20,000 Hz is only 0.67 inches (17 mm).
There is a special type of high-frequency sound wave beyond ultrasound: hypersound, which has frequencies above 107 MHz, or 10 trillion Hz. It is almost impossible for hypersound waves to travel through all but the densest media, because their wavelengths are so short. In order to be transmitted properly, hypersound requires an extremely tight molecular structure; otherwise, the wave would get lost between molecules.
Wavelengths of visible light, part of the electromagnetic spectrum, have a frequency much higher even than hypersound waves: about 109 MHz, 100 times greater than for hypersound. This, in turn, means that these wavelengths are incredibly small, and this is why light waves can easily be blocked out by using one’s hand or a curtain.
The same does not hold for sound waves, because the wavelengths of sounds in the range of human audibility are comparable to the size of ordinary objects. To block out a sound wave, one needs something of much greater dimensions— width, height, and depth—than a mere cloth curtain. A thick concrete wall, for instance, may be enough to block out the waves. Better still would be the use of materials that absorb sound, such as cork, or even the use of machines that produce sound waves which destructively interfere with the offending sound.
Amplitude and Intensity
Amplitude is critical to the understanding of sound, though it is mathematically independent from the parameters so far discussed. Defined as the maximum displacement of a vibrating material, amplitude is the “size” of a wave. The greater the amplitude, the greater the energy the wave
contains: amplitude indicates intensity, commonly known as “volume,” which is the rate at which a wave moves energy per unit of a cross-sectional area.
Intensity can be measured in watts per square meter, or W/m2. A sound wave of minimum intensity for human audibility would have a value of 10-12, or 0.000000000001, W/m2.As a basis of comparison, a person speaking in an ordinary tone of voice generates about 10-4,or 0.0001, watts. On the other hand, a sound with an intensity of 1 W/m2 would be powerful enough to damage a person’s ears.
REAL-LIFE APPLICATIONS
Decibel Levels
For measuring the intensity of a sound as experienced by the human ear, we use a unit other than the watt per square meter, because ears do not respond to sounds in a linear, or straight-line, progression. If the intensity of a sound is doubled, a person perceives a greater intensity, but nothing approaching twice that of the original sound. Instead, a different system—known in mathematics as a logarithmic scale—is applied.
In measuring the effect of sound intensity on the human ear, a unit called the decibel (abbreviated dB) is used. A sound of minimal audibility (10-12 W/m2) is assigned the value of 0 dB, and 10 dB is 10 times as great—10-11 W/m2.
But 20 dB is not 20 times as intense as 0 dB; it is 100 times as intense, or 10-10 W/m2.Every increase of 10 dB thus indicates a tenfold increase in intensity. Therefore, 120 dB, the maximum decibel level that a human ear can endure without experiencing damage, is not 120 times as great as the minimal level for audibility, but 1012 (1 trillion) times as great—equal to 1 W/m2, referred to above as the highest safe intensity level.
Of course, sounds can be much louder than 120 dB: a rock band, for instance, can generate sounds of 125 dB, which is 5 times the maximum safe decibel level. A gunshot, firecracker, or a jet—if one is exposed to these sounds at a sufficiently close proximity—can be as high as 140 dB, or 20 times the maximum safe level. Nor is 120 dB safe for prolonged periods: hearing experts indicate that regular and repeated exposure to even 85 dB (5 less than a lawn mower) can cause permanent damage to one’s hearing.
Production of Sound Waves
musical instruments. Sound waves are vibrations; thus, in order to produce sound, vibrations must be produced. For a stringed instrument, such as a guitar, harp, or piano, the strings must be set into vibration, either by the musician’s fingers or the mechanism that connects piano keys to the strings inside the case of the piano.
In other woodwind instruments and horns, the musician causes vibrations by blowing into the mouthpiece. The exact process by which the vibrations emerge as sound differs between woodwind instruments, such as a clarinet or saxophone on the one hand, and brass instruments, such as a trumpet or trombone on the other. Then there is a drum or other percussion instrument, which produces vibrations, if not musical notes.
Electronic Amplification
Sound is a form of energy: thus, when an automobile or other machine produces sound incidental to its operation, this actually represents energy that is lost. Energy itself is conserved, but not all of the energy put into the machine can ever be realized as useful energy; thus, the automobile loses some energy in the form of sound and heat.
The fact that sound is energy, however, also means that it can be converted to other forms of energy, and this is precisely what a microphone does: it receives sound waves and converts them to electrical energy. These electrical signals are transmitted to an amplifier, and next to a loudspeaker, which turns electrical energy back into sound energy—only now, the intensity of the sound is much greater.
Inside a loudspeaker is a diaphragm, a thin, flexible disk that vibrates with the intensity of the sound it produces. When it pushes outward, the diaphragm forces nearby air molecules closer together, creating a high-pressure region around the loudspeaker. (Remember, as stated earlier, that sound is a matter of fluctuations in pressure.) The diaphragm is then pushed backward in response, freeing up an area of space for the air molecules. These, then, rush toward the diaphragm, creating a low-pressure region behind the high-pressure one. The loudspeaker thus sends out alternating waves of high and low pressure, vibrations on the same frequency of the original sound.
The human voice
As impressive as the electronic means of sound production are (and of course the description just given is highly simplified), this technology pales in comparison to the greatest of all sound-producing mechanisms: the human voice. Speech itself is a highly complex physical process, much too involved to be discussed in any depth here. For our present purpose, it is important only to recognize that speech is essentially a matter of producing vibrations on the vocal cords, and then transmitting those vibrations.
Before a person speaks, the brain sends signals to the vocal cords, causing them to tighten. As speech begins, air is forced across the vocal cords, and this produces vibrations. The action of the vocal cords in producing these vibrations is, like everything about the miracle of speech, exceedingly involved: at any given moment as a person is talking, parts of the vocal cords are opened, and parts are closed.
The sound of a person’s voice is affected by a number of factors: the size and shape of the sinuses and other cavities in the head, the shape of the mouth, and the placement of the teeth and tongue. These factors influence the production of specific frequencies of sound, and result in differing vocal qualities. Again, the mechanisms of speech are highly complicated, involving action of the diaphragm (a partition of muscle and tissue between the chest and abdominal cavities), larynx, pharynx, glottis, hard and soft palates, and so on. But, it all begins with the production of vibrations.
Propagation: Does It Make a Sound?
As stated in the introduction, acoustics is concerned with the production, transmission (sometimes called propagation), and reception of sound. Transmission has already been examined in terms of the speed at which sound travels through various media. One aspect of sound transmission needs to be reiterated, however: for sound to be propagated, there must be a medium.
There is an age-old “philosophical” question that goes something like this: If a tree falls in the woods and there is no one to hear it, does it make a sound? In fact, the question is not a matter of philosophy at all, but of physics, and the answer is, of course, “yes.” As the tree falls, it releases energy in a number of forms, and part of this energy is manifested as sound waves.
Consider, on the other hand, this rephrased version of the question: “If a tree falls in a vacu-um—an area completely devoid of matter, including air—does it make a sound?” The answer is now a qualified “no”: certainly, there is a release of energy, as before, but the sound waves cannot be transmitted. Without air or any other matter to carry the waves, there is literally no sound.
Hence, there is a great deal of truth to the tagline associated with the 1979 science-fiction film Alien: “In space, no one can hear you scream.” Inside an astronaut’s suit, there is pressure and an oxygen supply; without either, the astronaut would perish quickly. The pressure and air inside the suit also allow the astronaut to hear sounds within the suit, including communications via microphone from other astronauts. But, if there were an explosion in the vacuum of deep space outside the spacecraft, no one inside would be able to hear it.
KEY TERMS
Acoustics: An area of physics devoted to the study of the production, transmission, and reception of sound.
Amplitude: The maximum displacement of a vibrating material. In wave motion, amplitude is the “size” of a wave, and for sound waves, amplitude indicates the intensity or volume of sound.
Cycle: For a sound wave, a cycle is a single complete vibration.
Decibel: A unit for measuring intensity of sound. Decibels, abbreviated dB, are calibrated along a logarithmic scale whereby every increase of 10 dB indicates an increase in intensity by a factor of 10. Thus if the level of intensity is increased from 30 to 60 dB, the resulting intensity is not twice as great as that of the earlier sound—it is 1,000 times as great.
Energy: The ability to perform work, which is the exertion of force over a given distance. Work is the product of force and distance, where force and distance are exerted in the same direction.
Frequency: In wave motion, frequency is the number of waves passing through a given point during the interval of one second. The higher the frequency, the shorter the wavelength. Measured in Hertz, frequency is mathematically related to wave speed, wavelength, and period.
Harmonic motion: The repeated movement of a particle about a position of equilibrium, or balance.
Hertz: A unit for measuring frequency, named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894). High frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per second) or megahertz (MHz; 106 or 1 million cycles per second.)
Intensity: Intensity is the rate at which a wave moves energy per unit of cross-sectional area. Where sound waves are concerned, intensity is commonly known as “volume.”
Longitudinal wave: A wave in which the movement of vibration is in the same direction as the wave itself. A sound wave is an example of a longitudinal wave.
Matter: Physical substance that has mass; occupies space; is composed of atoms; and is ultimately convertible to energy.
Medium: Material through which sound travels. (It cannot travel through a vacuum.) The most common medium (plural, media) of sound transmission experienced in daily life is air, but in fact sound can travel through any type of matter.
Oscillation: The vibration experienced by individual waves even as the wave itself is moving through space. Oscillation is a type of harmonic motion, typically periodic, in one or more dimensions.
Period: For wave motion, a period is the amount of time required to complete one full cycle. Period is mathematically related to frequency, wavelength, and wave speed.
Periodic motion: Motion that is repeated at regular intervals. These intervals are known as periods.
Rarefaction: A decrease in density.
Ultrasound : Sound waves with a frequency above 20,000 Hertz, which makes them inaudible to the human ear.
Vacuum: An area entirely devoid of matter, including air.
Wavelength: The distance between a crest and the adjacent crest, or the trough and an adjacent trough, of a wave. Wavelength, symbolized by X (the Greek letter lambda) is mathematically related to wave speed, period, and frequency.
Wave motion: A type of harmonic motion that carries energy from one place to another without actually moving any matter.
Reception of Sound
Recording
Earlier the structure of electronic amplification was described in very simple terms. Some of the same processes— specifically, the conversion of sound to electrical energy—are used in the recording of sound. In sound recording, when a sound wave is emitted, it causes vibrations in a diaphragm attached to an electrical condenser. This causes variations in the electrical current passed on by the condenser.
These electrical pulses are processed and ultimately passed on to an electromagnetic “recording head.” The magnetic field of the recording head extends over the section of tape being recorded: what began as loud sounds now produce strong magnetic fields, and soft sounds produce weak fields. Yet, just as electronic means of sound production and transmission are still not as impressive as the mechanisms of the human voice, so electronic sound reception and recording technology is a less magnificent device than the human ear.
How the ear hears
As almost everyone has noticed, a change in altitude (and, hence, of atmospheric pressure) leads to a strange “popping” sensation in the ears.Usually, this condition can be overcome by swallowing, or even better, by yawning. This opens the Eustachi-an tube, a passageway that maintains atmospheric pressure in the ear. Useful as it is, the Eustachi-an tube is just one of the human ear’s many parts.
The “funny” shape of the ear helps it to capture and amplify sound waves, which pass through the ear canal and cause the eardrum to vibrate. Though humans can hear sounds over a much wider range, the optimal range of audibility is from 3,000 to 4,000 Hz. This is because the structure of the ear canal is such that sounds in this frequency produce magnified pressure fluctuations. Thanks to this, as well as other specific properties, the ear acts as an amplifier of sounds.
Beyond the eardrum is the middle ear, an intricate sound-reception device containing some of the smallest bones in the human body— bones commonly known, because of their shapes, as the hammer, anvil, and stirrup. Vibrations pass from the hammer to the anvil to the stirrup, through the membrane that covers the oval window, and into the inner ear.
Filled with liquid, the inner ear contains the semicircular canals responsible for providing a sense of balance or orientation: without these, a person literally “would not know which way is up.” Also, in the inner ear is the cochlea, an organ shaped like a snail. Waves of pressure from the fluids of the inner ear are passed through the cochlea to the auditory nerve, which then transmits these signals to the brain.
The basilar membrane of the cochlea is a particularly wondrous instrument, responsible in large part for the ability to discriminate between sounds of different frequencies and intensities. The surface of the membrane is covered with thousands of fibers, which are highly sensitive to disturbances, and it transmits information concerning these disturbances to the auditory nerve. The brain, in turn, forms a relation between the position of the nerve ending and the frequency of the sound. It also equates the degree of disturbance in the basilar membrane with the intensity of the sound: the greater the disturbance, the louder the sound.
