Druyd:Knowledge

Transverse waves

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Mechanisms

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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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Parameters

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$E$

Modulus of Elasticity

$\nu$

Poisson coefficient

$G$

Shear module

$c_t$

c_t

Velocidad de la onda en el medio transmitido

m/s

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$\rho$

rho

Mean density

kg/m^3

$\tau$

tau

Torsion

$\gamma$

gamma

Twist angle

rad

Calculations

Equation

Number

First, select the equation:

, then, select the variable:

Calculations

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Equation

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Translated

Calculations

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Equation

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Translated

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Equation

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Equations

Equation

$c_t ^2 = \displaystyle\frac{ G }{ \rho }$

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

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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:

$\tau = G \gamma$

$G$

Shear module

$Pa$

5364

$\tau$

Torsion

$Pa$

5366

$\gamma$

Twist angle

$rad$

5367

where G is the so-called shear modulus.

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Shear Modulus

Equation

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

$E =2 G (1+ \nu )$

$E$

Modulus of Elasticity

$Pa$

5357

$\nu$

Poisson coefficient

$-$

5365

$G$

Shear module

$Pa$

5364

where G is the so-called shear modulus.

ID:(3772, 0)

Transverse speed of sound

Equation

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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

$c_t ^2 = \displaystyle\frac{ G }{ \rho }$

$\rho$

Mean density

$kg/m^3$

5088

$G$

Shear module

$Pa$

5364

$c_t$

Velocidad de la onda en el medio transmitido

$m/s$

9657

ID:(14181, 0)