# Standing wave energy

1. Jan 17, 2009

### atavistic

1. The problem statement, all variables and given/known data

A standing wave is maintained in a homogenous string of cross-sectional area a and density $$\rho$$ . It is formed by the superposition of two waves travelling in opposite directions given by the equations

y1 = Asin(wt-kx)
y2 = 2Asin(wt +kx)

Find the total mechanical energy confined between the section corresponding to the adjacent antinodes.

2. The attempt at a solution

The wave is given by y = Asin(wt-kx) + 2Asin(wt +kx)

KE of a small element is 1/2 u dx v^2 , where u = mass per unit length.

I find v by differentiating y wrt t.

Then I integrate with proper limits. But the integration looks outrageous looking at the simple answer. Is there any shortcut ? Also using above method we only get the KE, what about the PE?

2. Jan 17, 2009

### tiny-tim

Hi atavistic!
Show us!

3. Jan 17, 2009

### atavistic

Well can you tell me what I did is right or not and the thing about PE.