mechanisms

A variant to the longitudinal wave, in which the deformation is in the same direction of propagation, is when the deformation is perpendicular to the direction of propagation:

image

This type of wave is called a transverse wave. Since there are two axes perpendicular to the direction of propagation, there will be two transverse modes.

In the case of a solid, the transverse wave can be described as the lateral displacement of the atoms:

image

It should be noted that it is not a simple movement orthogonal to the translation, there is also a small displacement in the direction of propagation caused by the stresses of the 3D structure.

model

In the case of shear, the deformation is not associated with expanding or compressing, but with laterally offsetting the faces of a cube. The shear is therefore described by the angle \gamma with which it is possible to rotate the face perpendicular to the displaced surfaces. In analogy to Hook's law for compression and expansion, we have the relationship between torsion \tau and angle \gamma:

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where G is the so-called shear modulus.

The shear modulus G is related to the modulus of elasticity E and Poisson's ratio
u by

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where G is the so-called shear modulus.

If we compare the relationship of stress and strain

equation=8100

and the speed of sound (longitudinal)

equation=14179

with shear stress

equation=3771

so that a transverse speed of sound can be defined

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