Atmospheric acoustics

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The science of sound in the atmosphere. The atmosphere has a structure that varies in both space and time, and these variations have significant effects on a propagating sound wave. In addition, when sound propagates close to the ground, the type of ground surface has a strong effect.

Atmospheric sound attenuation

As sound propagates in the atmosphere, several interacting mechanism attenuate and change the spectral or temporal characteristics of the sound received at a distance from the source. The attenuation means that sound propagating through the atmosphere decreases in level with increasing distance between source and receiver. The total attenuation, in decibels, can be approximated as the sum of three nominally independent terms, as given in the equation below, where A_div is the attenuation due to geometrical divergence, A_air is the attenuation due to air absorption, and A_env is the attenuation due to all other effects and includes the effects of the ground, refraction by a nonhomogeneous atmosphere, and scattering effects due to turbulence.

Sound energy spreads out as it propagates away from its source due to geometrical divergence. At distances that are large compared with the effective size of the sound source, the sound level decreases at the rate of 6 dB for every doubling of distance. The phenomenon of geometrical divergence, and the corresponding decrease in sound level with increasing distance from the source, is the same for all acoustic frequencies. In contrast, the attenuation due to the other two terms in the equation depends on frequency and therefore changes the spectral characteristics of the sound.

Air absorption

Dissipation of acoustic energy in the atmosphere is caused by viscosity, thermal conduction, and molecular relaxation. The last arises because fluctuations in apparent molecular vibrational temperatures lag in phase the fluctuations in translational temperatures. The vibrational temperatures of significance are those characterizing the relative populations of oxygen (O₂) and nitrogen (N₂) molecules. Since collisions with water molecules are much more likely to induce vibrational state changes than are collisions with other oxygen and nitrogen molecules, the sound attenuation varies markedly with absolute humidity. See also Molecular structure and spectra; Viscosity.

The total attenuation due to air absorption increases rapidly with frequency. For this reason, applications in atmospheric acoustics are restricted to sound frequencies below a few thousand hertz it the propagation distance exceeds a few hundred meters. See also Sound absorption.

Effects of the ground

When the sound source and receiver are above a large flat ground surface in a homogeneous atmosphere, sound reaches the receiver via two paths. There is the direct path from source to receiver and the path reflected from the ground surface. Most naturally occurring ground surfaces are porous to some degree, and their acoustical property can be represented by an acoustic impedance. The acoustic impedance of the ground is in turn associated with a reflection coefficient that is typically less than unity. In simple terms, the sound field reflected from the ground surface suffers a reduction in amplitude and a phase change.

When the source and receiver are both relatively near the ground and are a large distance apart, the direct and reflected fields become nearly equal and cancel each other.

Refraction of sound

Straight ray paths are rarely achieved outdoors. In the atmosphere, both the wind and temperature vary with height above the ground. The velocity of sound relative to the ground is a function of wind velocity and temperature; hence it also varies with height, causing sound waves to propagate along curved paths.

The speed of the wind decreases with decreasing height above the ground because of drag on the moving air at the surface. Therefore, the speed of sound relative to the ground increases with height during downwind propagation, and ray paths curve downward. For propagation upwind, the sound speed decreases with height, and ray paths curve upward (see illustration). In the case of upward refraction, a shadow boundary forms near the ground beyond which no direct sound can penetrate. Some acoustic energy penetrates into a shadow zone via creeping waves that propagate along the ground and that continually shed diffracted rays into the shadow zones. The dominant feature of shadow-zone reception is the marked decrease in a sound's higher-frequency content. The presence of shadow zones explains why sound is generally less audible upwind of a source.

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Curved ray paths. (a) Refraction downward, during temperature inversion or downwind propagation. (b) Refraction upward, during temperature lapse or upwind propagation.

Refraction by temperature profiles is analogous. During the day, solar radiation heats the Earth's surface, resulting in warmer air near the ground. This condition is called a temperature lapse and is most pronounced on sunny days. A temperature lapse is the common daytime condition during most of the year, and also causes ray paths to curve upward. After sunset there is often radiation cooling of the ground, which produces cooler air near the surface. In summer under clear skies, such temperature inversions begin to form about 2 hours after sunset. Within the temperature inversion, the temperature increases with height, and ray paths curve downward.

The effects of refraction by temperature and wind are additive and produce rather complex sound speed profiles in the atmosphere.

Effects of turbulence

Turbulence in the atmosphere causes the effective sound speed to fluctuate from point to point, so a nominally smooth wave front develops ripples. One result is that the direction of a received ray may fluctuate with time in random manner. Consequently, the amplitude and phase of the sound at a distant point will fluctuate with time. The acoustical fluctuations are clearly audible in the noise from a large aircraft flying overhead. Turbulence in the atmosphere also scatters sound from its original direction. See also Turbulent flow.