Broadband sound reflection by plates covering side-branch cavities in a duct

Abstract

When a segment of a rigid duct is replaced by a plate backed by a hard-walled cavity, grazing incident sound waves induce plate bending, hence sound reflection. The mechanism is similar to the drumlike silencer with tensioned membranes [L. Huang, J. Acoust. Soc. Am. 112, 2014–2025 (2002)]. However, the logarithmic bandwidth over which the reflection occurs is much wider than that of a drumlike silencer of the same cavity geometry, the typical difference being nearly one octave band. The difference in the silencing performance is explained in terms of the intermodal acoustic interference between the odd and even in vacuo vibration modes. For a given cavity volume, the widest stopband for noise in air is obtained by using long plates with two free lateral edges parallel with the duct axis. The optimal material should be stiff and light, and the critical parameter is found to be the ratio of the Young’s modulus over the cube of density. Typically, this ratio is 250 times higher than those of common metallic materials like aluminum alloys, but it is within the reach of existing ultralight foam materials or composite beams with a light core.