Acoustic Bloch wave energy transport and group velocity

Abstract

The relationship between the steady‐state rate of energy transport and the group velocity is investigated for acoustic Bloch waves in a periodic waveguide. A time‐average energy flux relation is derived and used to find the energy transport velocity for an arbitrary periodic waveguide. An apparent disparity between the energy transport velocity and the power delivery is discussed. The group velocity is derived using a Bloch wave generalization of the usual Fourier transform method and is shown to be equal to the rate of energy transport. The integral transform method works well for the boundary value problem as the associated Bloch wave transform is relatively straightforward. The initial value problem, however, involves the inverse Bloch wave transform, the problems associated with which are discussed. [Work supported by the Office of Naval Research.]