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## Sound propagation in solids

Longitudinal and transverse waves can propagate in solids. If the solid is rod-shaped or plate-shaped, bending waves that are not pure longitudinal or transverse waves are also possible.

Pressure waves are pure longitudinal waves. The deflection consists of a shortening or stretching of the rod. Torsional waves, in which the movement consists in twisting the rod sections against each other, are pure transversal waves.

Longitudinal and transverse waves propagate at different speeds. The torsional modulus (see shear modulus) is included in the propagation speed of transverse waves (torsional waves).

$ctrans=Gρctrans = Speed ​​of propagation of the transverse wavesG = Shear, shear, torsion modulusρ = Density$

Longitudinal waves, on the other hand, are associated with a one-sided compression of the rod. This is where the modulus of elasticity comes in.

$clong=E.ρclong = Speed ​​of propagation of the longitudinal wavesE. = Modulus of elasticityρ = Density$

However, this equation is only valid as long as the transverse dimensions of the rod are small compared to the wavelength. The theory gives the following expression for the velocity of the longitudinal wave in an infinitely extended medium:

$clong=E.ρ·1-μ(1+μ)(1-2μ)clong = Speed ​​of propagation of the longitudinal wavesE. = Modulus of elasticityρ = Densityμ = Poisson's number$
Tab. 1
Velocities of sound in different media
materiallongitudinal in $ms-1$transversal in $ms-1$
air346-
Ethanol1207-
water1497-
Polyethylene920540
Polystyrene22401120
Air and liquids at 25 $° C$. The speed of longitudinal waves in solids is related to the formula (finite expansion of the solid). The speeds of sound in solids are dependent on their pretreatment.