Is there really no transverse sound wave in air? [duplicate]

Everything has some viscosity. The viscosity of the medium may support transverse wave, right?

So, is there really no transverse sound wave in air?

• A duplicate of this question Jan 9, 2016 at 14:11

$$v = \sqrt{\frac{G}{\rho}}$$
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.