Wave fronts for sound at developable surfaces (Q2717142)

This paper is dedicated to the investigation of sound fronts with respect to developable surfaces. Let a reflection surface and a source of sound be predefined. The locus of all points where the sound arrives after a given time interval (after having been reflected at the reflection surface) is another surface termed `sound front'. All such sound fronts (with varying time interval) make up a set of offset surfaces. One of these offset surfaces stands out and is called `central surface'. If the reflection surface is developable, the `central surface' is but a curve called `central curve'. It is the inverse problem which the author puts centre stage in this paper, namely for the case of developable reflection surfaces: If the central curve and the sound source are given, how can the developable reflection surface be reconstructed? The strategy and the results depend on whether the given curve is twisted or planar. Special cases like cones, second-order cones and the like are being discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0944.00034].