Show that the sound speeds for the following types of elastic waves in an isotropic material are in the ratios

The elastic waves are 

(i) Longitudinal waves along a rod, 

(ii) Longitudinal waves along a sheet, 

(iii) Longitudinal waves along a rod embedded in an incompressible fluid.

(iv) Shear waves in an extended solid.

(v) Torsional waves along a rod.

Transcribed Image Text:

1: (1 − v²)−1/² : ((1+y)(1-2v)) 1/2 : [2(1 + v)]-1/2 [2(1 + v)]-¹/2