Introduction to Sonar Transducer Design

1Acoustic Waves and Radiation

This chapter is devoted to issues affecting the acoustic environment in which sonar transducers are expected to perform. We will first review the linear theory of acoustics. We will then form the equations of force and motion and derive the Helmholtz wave equation. The Helmholtz wave equation will form the basis for most of the analyses conducted in this chapter. The wave equation is solved in the separable rectangular, spherical, and cylindrical coordinate systems. From these solutions, we derive the radiation patterns for spherical radiators and radiators located on cylindrical bodies. The Helmholtz integral formulations will then be reviewed as a prelude to our discussion into the far field beam patterns (BPs) of planar and linear apertures. We will also define the underlying assumptions in making the near field/far field distinctions. The concept of directivity and directivity index (DI) is reviewed next. In the next section, we will review issues affecting scattering and diffraction. Understanding diffraction is important in system design and especially hydrophone design. Radiation impedance, both self and mutual, is then reviewed. The discussion of the mutual radiation impedance between radiators is as close as we will get to a discussion on arrays. Finally, we will review transmission phenomena and the absorption and attenuation of sound. It is with the contents of this chapter that we have always started transducer design. We must understand ...