Speed of pressure wave propagation in flowing gas · RMPH 2016 #B1
Physics · fluid-mechanics
Problem
If the pressure in a layer of a macroscopically motionless gas system suddenly increases (by heating or rapid compression), the layer will begin to expand, compressing the adjacent layers. This pressure disturbance will be thus transmitted by contiguity as an elastic wave through the gas.
The speed c of this wave is the speed of its wavefront (the most advanced surface, the points of which oscillate in phase and the thermodynamic parameters of which have the same value). If in the reference frame of the unperturbed gas the process of the wave propagation is nonsteady (the gas parameters in any point vary with time), in the reference frame of the wavefront the process will be steady, so the simple equations for a steady state can be applied.
Derive the mathematical expression for the speed of the wavefront, taking into account that the thermodynamic parameters of the unperturbed gas are p1, ρ1, while those "behind" the wavefront are p2, ρ2.