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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marked as duplicate by Gert, Daniel Griscom, Kyle Kanos, user36790, Qmechanic♦ Jan 10 '16 at 1:50
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4$\begingroup$ A duplicate of this question $\endgroup$ – Victor Pira Jan 9 '16 at 14:11
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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.
answered Jan 9 '16 at 15:21
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$\begingroup$ John - all materials including gases have a bulk elasticity, right? So just considering your 2nd to last sentence, can't we somehow engineer some situation, perhaps under extreme conditions where energy gets stored, even for the most brief moment, to propagate a transverse wave? The model you wrote above considers linear properties, but there are non-linear effects in the propagation of waves - that I'm not totally familiar with. And I wonder whether this could lead to transverse waves - even if short lived. $\endgroup$ – docscience Jan 9 '16 at 16:26
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$\begingroup$ With no effective restoring force in a gas, they are indeed shortlived. Same problem with liquids, except at the surface, where gravity supplies the effective restoring force. $\endgroup$ – Peter Diehr Feb 18 '16 at 11:00
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