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Transverse wave
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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:
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.
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Transverse wave in a solid
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In the case of a solid, the transverse wave can be described as the lateral displacement of the atoms:
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.
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Model
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Calculations
Variable 
Given Calculate 
Target : Equation To be used 
Equations
$ c_t ^2 = \displaystyle\frac{ G }{ \rho }$
c_t ^2 = G / rho
$ E =2 G (1+ \nu )$
E =2* G *(1+ nu )
$ \tau = G \gamma $
tau = G * gamma
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Hooke's Law for the Case Shear
Equation
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
| $ \tau = G \gamma $ |
where
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Shear Modulus
Equation
The shear modulus
u
| $ E =2 G (1+ \nu )$ |
where
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Transverse speed of sound
Equation
If we compare the relationship of stress and strain
| $ \sigma = E \epsilon $ |
and the speed of sound (longitudinal)
| $ c ^2 = \displaystyle\frac{ E }{ \rho }$ |
with shear stress
| $ \tau = G \gamma $ |
so that a transverse speed of sound can be defined
| $ c_t ^2 = \displaystyle\frac{ G }{ \rho }$ |
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