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Everything has some viscosity. The viscosity of the medium may support transverse wave, right?
So, is there really no transverse sound wave in air?
This question already has an answer here:
Everything has some viscosity. The viscosity of the medium may support transverse wave, right?
So, is there really no transverse sound wave in air?
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The speed of a shear (transverse) wave is given by:
$$ v = \sqrt{\frac{G}{\rho}} $$
where $G$ is the shear modulus and $\rho$ is the density. In a gas the shear modulus is effectively zero, $G=0$, so the shear wave velocity is zero i.e. transverse waves don't propagate.
The viscosity affects the damping of a wave, but does not (directly) affect the propagation speed. It is true that a non-zero viscosity means there is a resistance to shear motion, but this is not enough to propagate a wave. For a transverse wave to propagate, the energy expended in shearing has to be stored elastically in the medium then returned as the wave passes by. This does not happen in a purely viscous medium.