Notes on Acoustics
Written by a noted authority in the subject area, this book is a comprehensive study of the theory and practical application of acoustics to numerous fields.
TABLE OF CONTENTS Notes on Acoustics
Chapter 4: Sound Reflection, Absorption, and Transmission
4.1 Introduction
In Chapters. 2 and 3, complex amplitudes were gradually introduced in the analysis of simple problems and it was mentioned that with increased problem complexity, the advantage of complex variables becomes more apparent. This will be further illustrated in this and subsequent chapters. Actually, after having become used to solving problems in this manner, it often becomes difficult to do it any other way.
4.1.1 Reflection, an Elastic Particle Collision Analogy
A ball thrown against a rigid wall bounces back with the same speed as the incident if the collision is elastic. This reflection is not unlike what happens when a sound wave strikes a rigid, impervious wall; it is reflected with no change in strength.
Consider next a head-on collision between an incident ball, the projectile, and a stationary ball, the target. The masses and initial velocities of these balls are M 1, M 2, and U 1, U 2. It is well known (from billiards, for example) that if the masses are the same, the projectile comes to rest after the collision and the target acquires the velocity of the projectile. [1] If the masses are not the same, we find the velocities 
and 
of the projectile and the target after the collision to be such that
These results follow from the equations for conservation of momentum and energy (see Problem 1). The quantities R U and T U can be considered to be reflection and transmission...
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