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Previous work has been done on the problem of the transmission of plane compressional elastic waves normally through a stratified medium consisting of alternate plane parallel layers of two different substances. Such a structure acts as a low-pass elastic wave filter. The present paper extends the analysis to the case of oblique transmission. This proves to be comparatively simple when the layer substances are both fluid. The transmission and attenuation (i.e., reflection) bands are found to depend on the angle of obliquity in a characteristic way. When one of the layer substances is solid, the problem is more difficult. Account must here be taken of the fact that compressional waves in the fluid layers give rise to both dilatational and shear waves in the solid layers. The result is somewhat more complicated than in the previous case but the structure still turns out to be a low-pass elastic wave filter for angles of obliquity less than the critical angle. As before the transmission and reflection bands are a function of the angle. In the special case in which the thickness of the solid layers is small compared with that of the fluid layers one obtains the elastic wave analog of the Bragg reflection law for x-rays, that is, one gets reflection approximately for the wave-lengths λn = 2l/n ⋅ sin θ, where l is the distance between successive solid layers and n is integral.
R. Bruce Lindsay (Sun,) studied this question.