Sound Propagation

Air is the common medium for sound propagation for human hearing. The molecules of air are in constant random motion and the density of the molecules dictates the static air pressure. If an object is vibrating in this space, the outward vibration of the object causes the molecules that the object initially makes contact with to be pushed in the direction of the object's outward motion. This will cause a condensing of the molecules, thus increasing the air molecule density at the location of the condensation. This increased density leads to an increase pressure. When the object moves in an inward direction air molecules will tend to fill the vacated space evenly (a property of the gas laws), resulting in a rarefaction of molecules and, hence, a lowering of the density of molecules. The lower density leads to a lower pressure. The distance between successive condensations (or rarefactions) is the wavelength (1) of sound, such that 1=c/f, where c is the speed of sound in the medium and f is frequency in hertz.

These areas of increased (condensations) and decreased (rarefactions) pressures of the sound wave radiate out from the vibrating source in a spherical manner. As the sound travels from the source the density at condensations and rarefactions decreases, since the area of the sphere is increasing. This results in a loss of pressure as the sound travels from the source, and this pressure loss is proportional to the distance squared (called the inverse square law).

In most spaces sound will encounter obstacles as it travels from its source to its destination. The sound wave can be absorbed at an obstacle's boundary, transmitted to the medium of the obstacle, reflected from the obstacle's surface, or diffracted around the obstacle. All these have significant consequences for hearing in the real world. For instance, a reflected sound wave may encounter the originating sound wave (or other reflections). The reflected wave may reinforce or cancel the originating sound wave. Locations of reinforcement will cause areas of increased sound pressure, whereas areas of cancellation lead to decreases in sound pressure. Often, the pattern of reinforcements and cancellations sets up a standing wave pattern such the standing wave vibrates at its resonant frequency causing enhanced intensity at this resonant frequency. The resonant frequency is inversely proportional to the size of the environment in which the standing wave occurs. This is the principal on which woodwinds, horns, and organ musical instruments operate. The pitch of the sound is proportional to the resonant frequency of the standing wave set up in the "pipe." Not only can standing waves exist in our acoustic environment but they can also exist in the ear canal and other parts of the auditory system.

In other cases, an object may cause a sound shadow in which there is an area of reduced pressure on the side of the object opposite from the sound source. The size of this sound shadow is a joint function of the wavelength of the sound and the size of the object such that to a first approximation sound shadows exist when the object's dimension are close to those of the sound's wavelength. The fact that the head produces a sound shadow plays a significant role in sound localization.

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