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A standing wavc is formed by two harmonic waves, y_1 = A sin (kx - omegat) and y_2= A sin(kx + omega t) travelling on a string in opposite directions. Mass density of the string is rho and area of cross - section is s. Find the total mechanical energy between two adjacent nodes on the string. |
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Answer» Solution :The distance between two adjacent nodes is `lambda/2 or pi/k`. `:.` Volume of string between two nodes will be V =(area of cross-section) (distance between two nodes) `=(s) = (pi/k)`.Energy density (energy per unit volume) of a TRAVELLING wave is GIVEN `U = 1/2 rho A^2 omega^2`. A standing wave is FORMED by two idential waves travelling in oposite directions. Therefore, the energy stored between two nodes in a standing wave E = 2[energy stored in a distance of `pi/k` of travelling wave] = 2 (energy density) (volume) `=2(1/2 rhoA^2 omega^2) ((pi s)/k) or E =(rho A^2 omega^2 pis )/k` |
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