- Key People:
- Hermann von Helmholtz
- Eric Zepler
News •
In addition to the geometric decrease in intensity caused by the inverse square law, a small part of a sound wave is lost to the air or other medium through various physical processes. One important process is the direct conduction of the vibration into the medium as heat, caused by the conversion of the coherent molecular motion of the sound wave into incoherent molecular motion in the air or other absorptive material. Another cause is the viscosity of a fluid medium (i.e., a gas or liquid). These two physical causes combine to produce the classical attenuation of a sound wave. This type of attenuation is proportional to the square of the sound wave’s frequency, as expressed in the formula α/f2, where α is the attenuation coefficient of the medium and f is the wave frequency. The amplitude of an attenuated wave is then given by
where Ao is the original amplitude of the wave and A(x) is the amplitude after it has propagated a distance x through the medium.
Table 5 gives sound-absorption coefficients for several gases. The magnitudes of the coefficients indicate that, although attenuation is rather small for audible frequencies, it can become extremely large for high-frequency ultrasonic waves. Attenuation of sound in air also varies with temperature and humidity.
| fluid | attenuation coefficient |
|---|---|
| helium | 52.5 |
| hydrogen | 16.9 |
| nitrogen | 133.0 |
| oxygen | 165.0 |
| air | 137.0 |
| carbon dioxide | 140.0 |
| water, at 0 °C (32 °F) | 0.569 |
| water, at 20 °C (68 °F) | 0.253 |
| water, at 80 °C (176 °F) | 0.079 |
| mercury, at 25 °C (77 °F) | 0.057 |
| methyl alcohol, at 30 °C (86 °F) | 0.302 |
Because less sound is absorbed in solids and liquids than in gases, sounds can propagate over much greater distances in these mediums. For instance, the great range over which certain sea mammals can communicate is made possible partially by the low attenuation of sound in water. In addition, because absorption increases with frequency, it becomes very difficult for ultrasonic waves to penetrate a dense medium. This is a persistent limitation on the development of high-frequency ultrasonic applications.
Most sound-absorbing materials are nonlinear, in that they do not absorb the same fraction of acoustic waves of all frequencies. In architectural acoustics, an enormous effort is expended to use construction materials that absorb undesirable frequencies but reflect desired frequencies. Absorption of undesirable sound, such as that from machines in factories, is critical to the health of workers, and noise control in architectural and industrial acoustics has expanded to become an important field of environmental engineering.
Diffraction
A direct result of Huygens’ wavelets is the property of diffraction, the capacity of sound waves to bend around corners and to spread out after passing through a small hole or slit. If a barrier is placed in the path of half of a plane wave, as shown in , the part of the wave passing just by the barrier will propagate in a series of Huygens’ wavelets, causing the wave to spread into the shadow region behind the barrier. In light waves, wavelengths are very small compared with the size of everyday objects, so that very little diffraction occurs and a relatively clear shadow can be formed. The wavelengths of sound waves, on the other hand, are more nearly equal to the size of everyday objects, so that they readily diffract.
Diffraction of sound is helpful in the case of audio systems, in which sound emanating from loudspeakers spreads out and reflects off of walls to fill a room. It is also the reason why “sound beams” cannot generally be produced like light beams. On the other hand, the ability of a sound wave to diffract decreases as frequency rises and wavelength shrinks. This means that the lower frequencies of a voice bend around a corner more readily than the higher frequencies, giving the diffracted voice a “muffled” sound. Also, because the wavelengths of ultrasonic waves become extremely small at high frequencies, it is possible to create a beam of ultrasound. Ultrasonic beams have become very useful in modern medicine.
The scattering of a sound wave is a reflection of some part of the wave off of an obstacle around which the rest of the wave propagates and diffracts. The way in which the scattering occurs depends upon the relative size of the obstacle and the wavelength of the scattering wave. If the wavelength is large in relation to the obstacle, then the wave will pass by the obstacle virtually unaffected. In this case, the only part of the wave to be scattered will be the tiny part that strikes the obstacle; the rest of the wave, owing to its large wavelength, will diffract around the obstacle in a series of Huygens’ wavelets and remain unaffected. If the wavelength is small in relation to the obstacle, the wave will not diffract strongly, and a shadow will be formed similar to the optical shadow produced by a small light source. In extreme cases, arising primarily with high-frequency ultrasound, the formalism of ray optics often used in lenses and mirrors can be conveniently employed.
If the size of the obstacle is the same order of magnitude as the wavelength, diffraction may occur, and this may result in interference among the diffracted waves. This would create regions of greater and lesser sound intensity, called acoustic shadows, after the wave has propagated past the obstacle. Control of such acoustic shadows becomes important in the acoustics of auditoriums.
Refraction
Diffraction involves the bending or spreading out of a sound wave in a single medium, in which the speed of sound is constant. Another important case in which sound waves bend or spread out is called refraction. This phenomenon involves the bending of a sound wave owing to changes in the wave’s speed. Refraction is the reason why ocean waves approach a shore parallel to the beach and why glass lenses can be used to focus light waves. An important refraction of sound is caused by the natural temperature gradient of the atmosphere. Under normal conditions the Sun heats the Earth and the Earth heats the adjacent air. The heated air then cools as it rises, creating a gradient in which atmospheric temperature decreases with elevation by an amount known as the adiabatic lapse rate. Because sound waves propagate faster in warm air, they travel faster closer to the Earth. This greater speed of sound in warmed air near the ground creates Huygens’ wavelets that also spread faster near the ground. Because a sound wave propagates in a direction perpendicular to the wave front formed by all the Huygens’ wavelets, sound under these conditions tends to refract upward and become “lost.” The sound of thunder created by lightning may be refracted upward so strongly that a shadow region is created in which the lightning can be seen but the thunder cannot be heard. This typically occurs at a horizontal distance of about 22.5 kilometres (14 miles) from a lightning bolt about 4 kilometres high.
At night or during periods of dense cloud cover, a temperature inversion occurs; the temperature of the air increases with elevation, and sound waves are refracted back down to the ground. Temperature inversion is the reason why sounds can be heard much more clearly over longer distances at night than during the day—an effect often incorrectly attributed to the psychological result of nighttime quiet. The effect is enhanced if the sound is propagated over water, allowing sound to be heard remarkably clearly over great distances.
Refraction is also observable on windy days. Wind, moving faster at greater heights, causes a change in the effective speed of sound with distance above ground. When one speaks with the wind, the sound wave is refracted back down to the ground, and one’s voice is able to “carry” farther than on a still day. When one speaks into the wind, however, the sound wave is refracted upward, away from the ground, and the voice is “lost.”
Another example of sound refraction occurs in the ocean. Under normal circumstances the temperature of the ocean decreases with depth, resulting in the downward refraction of a sound wave originating under water—just the opposite of the shadow effect in air described above. Many marine biologists believe that this refraction enhances the propagation of the sounds of marine mammals such as dolphins and whales, allowing them to communicate with one another over enormous distances. For ships such as submarines located near the surface of the water, this refraction creates shadow regions, limiting their ability to locate distant vessels.
Reflection
A property of waves and sound quite familiar in the phenomenon of echoes is reflection. This plays a critical role in room and auditorium acoustics, in large part determining the adequacy of a concert hall for musical performance or other functions. In the case of light waves passing from air through a glass plate, close inspection shows that some of the light is reflected at each of the air-glass interfaces while the rest passes through the glass. This same phenomenon occurs whenever a sound wave passes from one medium into another—that is, whenever the speed of sound changes or the way in which the sound propagates is substantially modified.
The direction of propagation of a wave is perpendicular to the front formed by all the Huygens’ wavelets. As a plane wave reflects off some reflector, the reflector directs the wave fronts formed by the Huygens’ wavelets just as a light reflector directs light “rays.” The same law of reflection is followed for both sound and light, so that focusing a sound wave is equivalent to focusing a light ray.
Reflectors of appropriate shape are used for a variety of purposes or effects. For example, a parabolic reflector will focus a parallel wave of sound onto a specific point, allowing a very weak sound to be more easily heard. Such reflectors are used in parabolic microphones to collect sound from a distant source or to choose a location from which sound is to be observed and then focus it onto a microphone. An elliptical shape, on the other hand, can be used to focus sound from one point onto another—an arrangement called a whispering chamber. Domes in cathedrals and capitols closely approximate the shape of an ellipse, so that such buildings often possess focal points and function as a type of whispering chamber. Concert halls must avoid the smooth, curved shape of ellipses and parabolas, because strong echoes or focusing of sound from one point to another are undesirable in an auditorium.
