Sound propagating in a moving medium is governed by a so-called convected wave equation. Consider the case where the background flow velocity is uniform in the x-direction with velocity V .
a. Following the procedure in Sect. 2.1, derive the convected wave equation for sound in a one-dimensional environment with flow velocity V:
Note that setting V = 0 gives the usual wave equation.
b. Show that this equation can also be derived from the standard wave equation by changing to a moving coordinate system
c. What is the form of this equation in three dimensions?