Fundamentals of Acoustics
Focusing on the analysis of acoustics in fluids, this book examines specific types of acoustic propagation in fluid media and the theoretical formulation of the problems rather than their practical aspects.
TABLE OF CONTENTS Fundamentals of Acoustics
Chapter 7: Diffusion, Diffraction and Geometrical Approximation
Following the example of Chapter 3, the objective of this chapter is to illustrate the integral formalism of linear problems of acoustics by considering situations the importance of which is recognized in acoustics and more generally in physics. Through these examples, some general laws are presented as well as few specific, but not unique, applications.
7.1. Acoustic Diffusion: Examples
The word diffusion comes from the Latin diffusio ( onis), meaning the action of spreading. This "spreading" concerns here the spatial distribution of acoustic energy from localized "sources".
7.1.1. Propagation in Non-Homogeneous Media
In a finite space occupied by a perfect fluid initially at rest, a limited domain (D) is considered non-homogeneous. Non-homogeneity is introduced as a small deviation of the characteristics of this space (density and compressibility coefficient) from those of the surroundings. Acoustics sources exterior to the domain (D) are assumed to generate an incident harmonic wave (incident to the domain D) and the Sommerfeld's condition at infinity is assumed to be satisfied.
The expression of the non-homogeneity of the fluid is introduced with the following notations:
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? E denotes the static density in the non-homogeneous domain (D),
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? 0 denotes the static density outside the domain (D) ,
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? ? = ? E - ? 0 is assumed relatively small and it is function of the point considered,
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? E denotes the coefficient of adiabatic compressibility of (D),
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? 0 denotes the coefficient of adiabatic compressibility outside the domain...
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