A point source of sound gives rise to a wave whose amplitude can be described by:

\[\delta=\left(\frac{B}{r}\right) \cos (\omega t-k r)\]

If the energy density per unit radial position associated with the wave is given by:

\[E=\frac{1}{2} ho A\left(\frac{\partial \delta}{\partial t}\right)^{2}\]

where \(A\) is the area through which the wave flows, show that the mean rate of transmission of energy across the surface of a sphere is given by:

\[2 \pi ho c k^{2} A^{2}\]