Geometric Acoustics

a branch of acoustics in which the laws of sound propagation are studied on the basis of the concept of sound rays, which may be regarded as lines along which acoustic energy is propagated. Geometric acoustics is the limiting case for wave acoustics when the wavelength becomes infinitesmal. Therefore, the methods of geometric acoustics are approximations—the shorter the wavelength, the more accurately they depict reality. The principal task of geometric acoustics is to calculate the trajectories of sound rays. The rays have the simplest form in a homogeneous medium in which they are straight lines. The equations for geometric acoustics have essentially the same form as those for geometric optics. The same laws of reflection and refraction hold for sound rays as for light rays.

Practical applications of the methods of geometric acoustics are made in very different areas of acoustics. For example, in architectural acoustics the rectilinear properties of sound rays make it possible to determine reverberation time in a very simple way. The operation of fathometers and hydrolocators is based on measurements of the time it takes for sound rays to travel to a reflecting object and back. The ray concept is used in designing sound focusing systems. An approximate theory for sound propagation in nonhomogeneous media (such as the ocean and the atmosphere) has been developed on the basis of the laws of geometric acoustics.

The methods of geometric acoustics have a limited field of application because the ray concept itself is only valid for those cases where the amplitude and direction of a wave undergo little change over distances in the order of the length of a sound wave. Specifically, when using geometric acoustics it is necessary that the dimensions of the rooms or obstacles in the sound path should be many times greater than the wavelength. If the characteristic dimension for a given problem becomes comparable to the wavelength, then wave diffraction begins to play an important part, and this is not covered by geometric acoustics.