An attempt has been made to develop a method for dealing with solutions of problems connected with the production of waves by spherical concentrations of compressed air. Starting from the general equations for three-dimensional spherically symmetrical flow in a homogeneous compressible medium having constant entropy everywhere, a process has been devised to apply step-by-step calculations over small intervals of time to investigate the general features of such a motion. A complete solution has been worked out in one particular case for a not very intense initial distribution of pressure, and various indirect checks have indicated that the results are reasonably accurate. These results show m any features of definite interest. As distinct from plane or spherical sound wave theory, it is found that a train of waves passes away from the centre of disturbance, the amplitudes and wave lengths falling off from wave to wave. Furthermore, as distinct from finite amplitude plane wave theory which shows that any wave must eventually become a shock wave, the waves obtained in the finite amplitude spherical wave case show no indication of becoming shock waves, and indeed show towards the closing stages of the calculation a similarity to sound wave propagation. The method is applicable to any spherically symmetrical motion up to such a time as the formation of a shock wave takes place and then fails owing to the assumption of constant entropy.
A Study of Finite Amplitude Distortion of a Sound Wave in Air