SOUND PROPAGATION IN ONE-DIMENSIONAL UNSTEADY FLOW

The wave equation in one-dimensional unsteady flow was derived, basing on momentum equation, continuity equation and energy equation etc.. It is a second-order linear hyperbolic partial differential equation with Mach number M and ∂M/∂t terms. The solution of this equation has been obtained. Some results were obtained by the present analyses. When a harmonic wave propagates in one-dimensional unsteady flow, the wave amplitude at any x-position will be related with Mach number M and ∂M/∂t. This relationship will tend towards a limit, when propagation distance is long enough.
It is also a nonlinear phenomenon in frequency domain obviously. The harmonic wave will become a wide band wave when it propagates in the unsteady flow.