Spherical Sound Waves of Finite Amplitude

Abstract

Nonlinear effects in the propagation of sound waves produced by a sinusoidally pulsating sphere have been studied theoretically. Various approximation methods have been found useful for different ranges of the parameters and at different distances from the source. Harmonic distortion generated in the field relatively near the source can be determined from a conventional perturbation solution. This solution has been developed in a form which permits numerical computation of the Fourier coefficients to terms of fourth order in the amplitude. At larger distances, this solution fails to converge, but a perturbation in terms of the characteristics of the partial differential equations is quite useful. Neglecting absorption, it is found that in spite of spherical divergence, which tends to retard the increase of distortion, the wave always evolves into an iterated shock wave at a finite distance, although a very great one for weak sources. The distance at which shocks are formed and the attenuation of the iterated shock wave as it propagates have been calculated for various examples. The work was supported by contract USAF 33 (616)-2772 with the Aero Medical Laboratory at Wright Air Development Center.