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Q.

The wave function of a triangular wave pulse is defined by the relation below at time t = 0 sec.y=mx for 0≤x≤a2−m(x−a) for a2≤x≤a0 every where else The wave pulse is moving in the +X direction in a string having tension T and mass per unit length μ . The total energy present with the wave pulse is  m2Ta×p, then p is____

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Detailed Solution

dU=12Tdxdydx2 ⇒U=12T∫0a2m2dx+∫a2am2dx=m2Ta2Velocity of particle=vP=dydt=slope×wave velocity=mTμ dK=12μdxdydt2=12μdxmTμ2⇒K=12T∫0am2dx=m2Ta2∴Total energy=U+K=m2Ta
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