Consider a small part of the total

Consider a small part of the total surface of the sphere, of area S, and having a circular boundary(in cross-section, fig.1(b)). Since it is surrounded by other areas vibrating similarly, it may be regarded as driving a conical tube whose apex is the centre of the sphere. Suppose the radius of S to be 0.05 wavelength and that at a point a further 0.05 wavelength away is asurface S1. Since the two surfaces are vibratingonly 18° out of phase (0.05 of a cycle) the air volume between them may be treated as almost incompressible, rather like a liquid, and therefore the volume S1 must equal that displacedat S. Since S1 is four times the area of S(proportional to square of distance from spherecentre)the velocity at S1 will be l/4 that at S. Now, the kinetic energy of a given thin layer of air is proportional to its area multiplied by the square of its velocity. So, the energy passing through S1 is only 1/4 of that at S, the remainder being stored in the intervening air mass.