Freaking Out Entanglement

What if we do replace the factor of $\cfrac{1}{3}$ that results from considering only one of the three dimensions in space,

$3*P=3*\cfrac{2}{3}\rho_n*\cfrac{4}{3}\pi{(2c)^3}*\cfrac{1}{2}m_av^2_{rms}$

and instead consider a volume in 3D space.

We have,

$\rho_n=\cfrac{dn_s}{df}=\cfrac{8\pi}{c^3}f^2$

$P=3*\cfrac{2}{3}*\cfrac{8\pi f^2}{c^3}*\cfrac{4}{3}\pi{(2c)^3}*\cfrac{1}{2}m_av^2_{rms}$

\(\cfrac{8^3}{6}\pi^2*f^2*m_ac^2=1*\cfrac{4}{3}\pi*f^3*m_ac^2\)

\(f=64*\pi=201.06\,Hz\)  wrong!

Are we done?  Don't freak out with $67.02\,Hz$,  do $201.06\,Hz$...

It won't turn off???