High frequency scattering from spherical shells and internal reflection resonances

It is shown that it is possible to excite very large return signals at frequencies corresponding to values at which the (half)/integral wave lengths (due to the dilatational wave of the material) are equal to the shell thickness. At those values the longitudinal (shear) waves are transparent to the shell and reflect from the inner surface. The reflected signals add coherently with the specularly scattered signal yielding a large return. The upper limit of the resonance may be found by the flat plate limit for the shell thickness. A partial wave study shows that the prediction and interpretation of these events is valid. Further, these resonances prove to correspond to the S₁ Lamb resonance