The Diffraction of a Sound Wave by an Infinite Set of Plates Available to Purchase

It is pointed out that a certain class of diffraction problems can be formulated as Wiener‐Hopf integral equations [R. E. A. C. Paley and N. Wiener, “The Fourier transform in the complex domain,” Am. Math. Soc. Colloq. Pub. 19 (1934), Ch. IV] and solved exactly, an observation due to Schwinger [J. F. Carlson and A. E. Heins, Q. App. Math. 4, 313 (1947)]. Following the analysis of the equivalent electromagnetic problem by Carlson and Heins [Q. App. Math. 5, 82 (1947)], the diffraction of a plane wave of sound by an infinite set of parallel equally spaced semi‐infinite plates is calculated. The conditions for plane wave propagation within the plates, for a single reflected wave, and expressions for the reflection and transmission coefficients are given. Except for the limitations by the requirements that only a plane wave be propagated and that there be only a single reflected wave, the reflection and transmission coefficients are found to be independent of wave‐length or the spacing between the plates. Other problems which may be solved by the same techniques are cited.