(a)[2]
The intensity of a progressive wave is the mean power passing through a surface per unit area. Show that the SI base units of intensity are $\text{kg s}^{-3}$.
(b(i))[2]
The intensity $I$ of a sound wave is linked to the amplitude $x_0$ by $I = K \rho c f^{2} x_0^{2}$, where $\rho$ is the density of the medium through which the sound is passing, $c$ is the speed of the sound wave, $f$ is the frequency of the sound wave and $K$ is a constant. Show that $K$ is dimensionless.
(b(ii))[3]
Calculate the intensity, in $\text{pW m}^{-2}$, for a sound wave with $K = 20$, $\rho = 1.2$ in SI base units, $c = 330$ in SI base units, $f = 260$ in SI base units and $x_0 = 0.24\,\text{nm}$.