II. The propagation of sound waves in an open-ended channel

Abstract

An exact solution is obtained for the problem of a harmonic wave of sound approaching the open end of a two-dimensional channel, and suffering reflection and transmission. Within a certain wavelength range, the wave returning along the channel becomes sensibly plane at large distances from the mouth, the reflection coefficient being exp [-2πb/λ], where 2b is the width of the channel and λ is the wavelength. Explicit formulæ are also obtained for the change of phase in the returning wave, and for the transmitted energy. It is also shown that the solution can be used to deduce the energy absorbed froln a plane wave external to the channel and approaching from an arbitrary direction.