ABSTRACT
There are many advantages in using plane wave solutions; they are conceptually simple and greatly facilitate the mathematics. However, in practice, ultrasonics always involves the use of finite size transducers, hence finite beams. The circular piston radiator is an important example in ultrasonics as it is about the simplest approximation that can be made for radiation into an infinite medium. It is also important in audio acoustics in the theory of loudspeakers. The assumption will be made that it is mounted inside an infinite baffle, so that sound is only radiated in the forward direction. Scattering of acoustic waves by obstacles of various sorts is, as in most branches of physics, a highly developed and mathematically very sophisticated subject. There are several levels of treatment for focused acoustic waves. The simplest, level 1, is to use geometrical optics or ray theory.
