Answer
$$5.89\times10^{-9}\;m$$
Work Step by Step
Here, time period of the wave is: $T=2\;ms$
And pressure amplitude is: $\Delta p_m=8\;mPa=8\times10^{-3}\;Pa$
So the angular frequency of the wave is given by:
$\omega=\frac{2\pi}{T}=\frac{2\pi}{2\times10^{-3}}\;rad/s=\pi\times10^3\;rad/s$
The pressure amplitude is calculated using the formula:
$\Delta p_m= (v\rho \omega)s_m$
or, $s_m=\frac{\Delta p_m}{v\rho \omega}$
substituting the given values
$s_m=\frac{8\times10^{-3}}{320\times1.35\times\pi\times10^3}\;m$
or, $\boxed{s_m=5.89\times10^{-9}\;m}$
