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atavistic
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Homework Statement
A standing wave is maintained in a homogenous string of cross-sectional area a and density [tex]\rho[/tex] . It is formed by the superposition of two waves traveling 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?