On the acoustics of a coupled space

An examination of acoustic wave propagation in a coupled space is presented. The analysis presented is limited to the first two longitudinal modes of the cavity. It is shown that the spacial behavior of the modes of vibration in the cavity is affected by the coupling discontinuity. The degree with which the discontinuity influences the pressure variation is parametrized by a single small parameter ɛ, where ɛ is the ratio of the typical cavity height, H₀ to the cavity length L 0. An approximate solution for the pressure in the space is obtained using the method of matched asymptotic expansions. Experimental results are also presented as verification of the theoretical results.