  For more than 20 years, observation of the non-dissipative Hall viscosity in
the quantum Hall effect has been impeded by the difficulty to probe directly
the momentum of the two-dimensional electron gas. However, in three-dimensional
systems such as superfluid ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$, the momentum
density is readily probed through transverse acoustic waves. We show that in a
three-dimensional elastic medium supporting transverse waves, a non-vanishing
Hall viscosity induces circular birefringence. Such an effect has been observed
in ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ in the presence of a weak magnetic
field, and is known as the acoustic Faraday effect. The acoustic Faraday effect
has been understood in terms of the Zeeman splitting of the excited order
parameter modes which support the transverse wave propagation in the
superfluid. We show that the Zeeman effect can generically lead to a non-zero
Hall viscosity coefficient, and confirm this prediction using a simple
phenomenological model for the ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$
collective modes. Therefore, we claim that the observation of the acoustic
Faraday effect can be leveraged to make a direct observation of the Hall
viscosity in superfluid ${}^{3}\mathrm{He}\!\!-\!\!\mathrm{B}$ in a magnetic
field and other systems such as the crystalline
$\mathrm{Tb}_{3}\mathrm{Ga}_{5}\mathrm{O}_{12}$ material.
