Abstract

Although we normally think of acoustic waves as travelling `at the speed of sound’,  nevertheless there are perfectly good `subsonic waves’ which can travel at any speed less than this.  Such waves are often called `inhomogeneous’, because their amplitude necessarily varies in the transverse direction, and they are essential for describing near fields (and also edge waves).  From this familiar starting point, I shall present the complete ray structure of a number of three-dimensional fields which I believe are not well-known, despite being of fundamental importance to multiple wave scattering problems.   These suggest a number of new canonical scattering problems in which a highly geometric ray theory approach is possible for determining fine details of scattering in the near- and mid-field.  A basic object for our purposes is the three-dimensional near-field ray structure of a high-order rotating multipole.  The near field is a `spinning orange’, somewhat flattened to ellipsoidal shape, in which the segments are  regions of alternating high and low pressure, and the `peel’ marks the transition to propagating spiral waves in the far field.  Although this structure is easily deducible from the Debye approximation to a Hankel function of arbitrary order, I believe it will not be known to everyone in the audience. I’ll report on the first steps of progress with the new canonical problems, begun in collaboration with Stuart Hawkins in this Multiple Wave Scattering programme.  It seems certain that the new geometrical structures disclosed by the numerical codes will all yield to a high-precision analytical description in the fullness of time.