Physics Asked by user714852 on December 23, 2020
I am simulating the propagation of an acoustic field through elastic media. I have identified a pocket of shear stress which is travelling with a speed very close to that of the longitudinal wave speed in the medium (glass optical fibre). The shear wave speed of glass is considerably lower than the measured velocity.
My silly question is: is there any way a longitudinal wave can have a shear velocity component? I’m guessing not, so the follow up is: what kind of wave could this be? It’s not in a plate and is not close to the shear velocity so that rules out Rayleigh, Love, Lamb, etc. Are there any other types of exotic wave that fit this criteria?
If your material is anisotropic you don't have transverse and longitudinal waves anymore. Instead, you have quasi-transverse and quasi-longitudinal ones. That means that they are not orthogonal/parallel to the wave vector but close to.
Furthermore, the speed of the wave depends on the direction and in some directions the quasi-transverse speed can be higher than the quasi-longitudinal.
Answered by nicoguaro on December 23, 2020
Longitudinal waves in a rod (or glass fibre) travel at a speed given by Young's modulus, and as well as longitudinal motion the rod gets thicker or thinner as the wave travels. There is therefore some transverse motion and if the longitudinal strain is $e_{xx}$ then the transverse strain is $e_{xx}=e_{yy}=- sigma e_{zz}$ with $sigma$ being Poisson's ration. There is no off diagonal stress in these coordinates, but the shear modulus is involved in determining the speed.
Answered by mike stone on December 23, 2020
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