The eqn and proof of energy of sinosiodal waves.

[Wen]

I was asked to give the eqn and proof of energy of sinosiodal waves.
However, I only know the enq of sinosiodal waves on string and to prove it.

Energy= 1/2 (mass per unit length).(ang. freq.)^2.(amplitude)^2.wavelength

So what is the eqn of energy of general wave. It is should be almost identical to the eqn above.
But what about the mass per unit length. What replaces it?
Is it multiplied with wavelength to give the mass of particle per wavelength?That's merely guessing?
Could anymore tell me the answer?

 

[lightgrav]

mass/length * length/wave = mass/wave .

Because wA is MAXIMUM speed of the string,
(using w=omega) you need another factor 1/2
to get the average KE in ONE WAVE.
In order to oscillate, the system must be able
to shift Energy from KE to PE and back to KE,
so the Energy spends half its time as PE.
So the average PE in one wave is 1/2 your formula.

Therefore, your formula is KE + PE = Etotal PER WAVE .

If your general wave spreads out sideways,
replace your mass/length with mass/area,
and your wavelength with wavelength*width.

If your wave spreads out vertically also,
use mass/Volume and wavelength*width*height.

 

[quasar987]

What about for an electromagnetic wave? To quote Wen,

[...] what about the mass per unit length. What replaces it?