What is the equation for calculating energy carried by a wave?

[yoq_bise]

Hi all,
In all books I looked it is written that energy carried by a wave is proportional to its amplitudes square

i.e.
E$$\propto$$A², if wave equation is f(x)=Asin(wx)

but what is the exact equation?

Also if we define the wave with Fourier series

f(x)=$$\sum$$Acos(nx)+Bcos(nx)

what would be the energy carried by this wave?

 

[wywong]

E$$\propto$$A², if wave equation is f(x)=Asin(wx)

but what is the exact equation?

To be proportional, you expect $$E=kA^2$$. k depends on the type of wave and type of medium.

Also if we define the wave with Fourier series

f(x)=$$\sum$$Acos(nx)+Bcos(nx)

what would be the energy carried by this wave?

I suppose you meant $$\sum Acos(nx)+Bsin(nx)$$.

$$E=k\sum{(A^2+B^2)}$$

if k is independent of frequency. Otherwise

$$E=\sum{k(A^2+B^2)}$$

 

[KickKat]

this is a little off topic, but I'm doing a project and i need to know some infrastructure issues with tidal wave energy generation, and i don't know of any, help please?

 

[berkeman]

this is a little off topic, but I'm doing a project and i need to know some infrastructure issues with tidal wave energy generation, and i don't know of any, help please?

Well, what other uses of the ocean are there that might be in conflict with wave energy extraction devices? And what kind of infrastructure would be necessary to convert the energy to electrical grid power, and how would you get it to the grid?

Look at the various proposals for (and some actual installed) wave power extraction facilities, and think about those issues I mentioned above...