End correction at the interface between a plain and a perforated pipe

This paper considers the plane-wave end correction that should be applied at the junction between a plain and a perforated pipe of equal diameter in the absence of mean flow. A general theory is developed that results in an equation for the end correction of all such junctions. The theory is verified by experimental results for the end correction obtained via the measurement of resonant frequency of a Helmholtz resonator whose neck is formed of a plain section and then a perforated section of pipe, before termination into free space. It is shown that in most practical situations within automotive silencers the perforated pipe will be long enough for the nature of the termination to be irrelevant. A simple formula is developed to evaluate this long-length limit and from it the dependence of the end correction upon all the parameters within the problem becomes explicit.