Shear modulus effect on acoustically transparent materials

Materials have been developed that match density
p
and dilatational sound speed
c
to the values of water as closely as possible while maintaining sufficient rigidity to serve for structural purposes. Matching of density and speed results in transparency for fluids only; the shear modulus in a solid admits the presence of a shear wave which causes deviation from ideal
pc
behavior. The effect of a finite shear modulus on the reflection of plane waves by an infinite plane is analyzed. The shear modulus of the material was measured following a method developed by R. L. Adkins in 1966. Examples are given of the reflection coefficient as a function of incidence angle for values of
p
and
c
close to those of the medium, and various ratios of plate thickness to dilatational wavelength. The condition of total reflection is shown to be related to the occurrence of thickness-shear resonances. Insertion-loss measurements on a structurally rigid
pc
panel are compared with results of the analysis.