Reflection and Transmission of Sound by a Moving Medium: A Simple Aerodynamic Interpretation

Abstract

Significant reflection and refraction occur for sound waves incident at an interface between moving streams. An analysis is made for plane waves (not necessarily periodic) impinging on a plane interface. The analysis and the physical interpretation are both simplified by using axes moving with the speed of the ripple that must develop in the interface. The acoustic problem is thus changed into the aerodynamic problem of the flows above and below a wavy wall (the rippled interface). In this view the angles of incidence and refraction are regarded as the respective Mach angles in two supersonic streams. The velocity difference between these streams is identical with that of the original two streams. The known angle of incidence thereby leads immediately to an equal angle of reflection and a simply related angle of refraction. The angle of refraction is imaginary when the associated velocity, calculated by the velocity-difference rule, is subsonic; this is a condition of total reflection. Strengths of the reflected and refracted waves are evaluated in simple form by application of compatibility conditions at the interface; these are believed to correct an error found in Keller's work. In particular, a region of strong amplification of the reflected waves is predicted.