Acoustic Wavefields

Abstract

This chapter is concerned with acoustic radiators and scatterers of cylindrical and spherical shape which forms the basis for the discussion of wavefield decomposition to be detailed in Chapter 3. Acoustic wavefields in cylindrical and spherical coordinate systems are considered that travel through a fluid, most notably air, and that interact with objects and structures resulting in scattering phenomena. In order to arrive at tractable mathematical descriptions of problems related to acoustic radiation and scattering a few basic assumptions are introduced here [JF93]:

• 1. All fluids and materials considered are assumed to obey linear equations. This restriction limits the following discussions to small-signal disturbances of the transmitting medium.

• 2. The media the acoustic wavefields interact with are assumed to be homogeneous.

• 3. Steady-state conditions are assumed which means that initial transient effects can be neglected.

• 4. For scattering problems, only local interactions between a wavefield propagating in a homogeneous medium and bodies within this medium are assumed.

It should be noted that all of the above assumptions are reasonably standard in many textbooks on linear acoustics, such as [MI68], [JF93], [Wil99] and [Bla00].