On the acoustical implications of vortex shedding from an exhaust pipe

Asymptotic approximations for small Strouhal number are derived for the solution of the problem of the interaction between an acoustic wave and a subsonic jet flow issuing from a semi-infinite pipe. Density and sound speed differences between the jet flow and the (slowly moving) ambient medium, and a general edge condition are included. The approximations relate to the field inside the jet flow, to the far field, to the reflection coefficient, end-impedance and end correction for the reflected wave inside the pipe, and to the transmitted and radiated sound power. Within the range of parameters considered, the effect of the density and sound speed differences and ambient flow is found to be appreciable, although the character of the solution is not changed. However, the choice of the edge condition does have important implications; specifically the phase of the reflected wave is most sensitive to only slight deviations from the Kutta condition.