On the acoustic shadow of a sphere. With an Appendix, giving the values of Legendre's functions from P0 to P20 at intervals of five degrees.

Abstract

The problem here considered is that of the intensity of sound at the various points of a rigid and fixed sphere on which plane waves impinge, or reciprocally the intensity at a distance in various directions due to a source of sound situate upon the surface of the sphere. The analytical solution is readily given, but in the interpretation everything depends upon the ratio of the wave-length (2π/k) to the circumference (2πc). If kc be small, the sphere has little effect. In my book on the “Theory of Sound,” 328, I have considered (but only for certain special directions) the case of kc = 2. The extension to various directions is now given; and the calculation is pushed to the case of kc = 10, about as far as is practicable. For this purpose the values of Legendre’s Functions up to P20 are required.