Answer
The initial wave amplitude is $~~70~nm$
Work Step by Step
In part (a), we found that the initial sound intensity is $I = 10^{-5}~W/m^2$
We can find the initial wave amplitude:
$I = \frac{1}{2}\rho v \omega^2~s_m^2$
$s_m^2 = \frac{2I}{\rho v \omega^2}$
$s_m = \sqrt{\frac{2I}{\rho v \omega^2}}$
$s_m = \sqrt{\frac{2I}{\rho v (2\pi f)^2}}$
$s_m = \sqrt{\frac{(2)(10^{-5}~W/m^2)}{(1.21~kg/m^3)(343~m/s) (2\pi)^2(500~Hz)^2}}$
$s_m = 7.0\times 10^{-8}~m$
$s_m = 70~nm$
The initial wave amplitude is $~~70~nm$.
