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# Acoustics

## Transmission Of Sound

In order for sound to travel between the source and the receiver there must be some material between them that can vibrate in the direction of travel (called the propagation direction). (The fact that sound can only be transmitted by a material medium means that an explosion outside a spaceship would not be heard by its occupants!) The motion of the sound-producing body causes density variations in the medium (see Figure 5, which schematically shows the density variations associated with a sound wave), which move along in the direction of propagation. The transmission of sounds in the form of these density variations is termed a wave since these variations are carried forward without significant change, although eventually friction in the air itself causes the wave to dissipate. (This is analogous to a water wave in which the particles of water vibrate up and down, while the "wave" propagates forward.) Since the motion of the medium at any point is a small vibration back and forth in the direction in which the wave is proceeding, sound is termed a longitudinal wave. (The water wave, like the violin string, is an example of a transverse wave.) The most usual medium of sound transmission is air, but any substance that can be compressed can act as a medium for sound propagation. A fundamental characteristic of a wave is that it carries energy and momentum away from a source without transporting matter from the source.

Since the speed of sound in air is about about 1,088 ft/sec (331 m/sec), human speech involves wavelengths from about 1.3 in to 11 ft (3.3 cm to 3.3 m). Thus, the wavelengths of speech are of the size of ordinary objects, unlike light, whose wavelengths are extremely small compared to items that are part of everyday life. Because of this, sound does not ordinarily cast "acoustic shadows" but, because its wavelengths are so large, can be transmitted around ordinary objects. For example, if a light is shining on a person, and a book is placed directly between them, the person will no longer be able to see the light (a shadow is cast by the book on the eyes of the observer). However, if one person is speaking to another, then placing a book between them will hardly affect the sounds heard at all; the sound waves are able to go around the book to the observer's ears. On the other hand, placing a high wall between a highway and houses can greatly decrease the sounds of the traffic noises if the dimensions of the wall (height and length) are large compared with the wavelength of the traffic sounds. Thus, sound waves (as for all waves) tend to "go around" (e.g., ignore the presence of) obstacles which are small compared with the wavelength of the wave; and are reflected by obstacles which are large compared with the wavelength. For obstacles of approximately the same size as the wavelength, waves exhibit a very complex behavior known as diffraction, in which there are enhanced and diminished values of the wave amplitude, but which is too complicated to be described here in detail.

The speed of sound in a gas is proportional to the square root of the pressure divided by the density. Thus, helium, which has a much lower density than air, transmits sound at a greater speed than air. If a person breathes some helium, the characteristic wavelengths are still determined by the shape of the mouth, but the greater sound speed causes the speech to be emitted at a higher frequency—thus the "Donald Duck" sounds from someone who speaks after taking a breath of helium from a balloon.

In general, the speed of sound in liquids is greater than in gases, and greater still in solids. In sea water, for example, the speed is about 4,750 ft/sec (1,447 m/sec); in a gas, the speed increases as the pressure increases, and as the density decreases. Typical speeds of sound in solids are 5,450 yd/sec (5,000 m/sec), but vary considerably from one solid to another.