Mean Energy and Momentum Effects in Waves

Abstract

Although energy is a second-order quantity in acoustics (and therefore very small), it is important because there is a fundamental conservation law for energy and also because energy considerations are most useful for deriving equations of motion. An important application of the conservation law in acoustics is the Statistical Energy Analysis (SEA) (see Chapter 8). The most common example of the use of energy methods for deriving equations of motion is the application of Hamilton’s principle (or some related energy principle). This is equivalent to the statement that, subject to the initial and boundary conditions, the motion of a system is such that the mean difference between kinetic and potential energy is as small as possible (Morse & Feshbach 1953) (see also Rayleigh’s principle in Chapter 20).