Equation of a transeverse wave propagating in a string is y=2sin50πt−10πxmm. Where x is in metre. If at t = 0, elastic potential energy stored in the string at x = 10/4 cm is 2 J/m, what is the elastic potential energy stored in the string at x = 10/3 cm?
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a
1 J/m
b
6 J/m
c
8 J/m
d
4 J/m
answer is D.
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Detailed Solution
y=2sin50πt−10πxmm∴ ∂y∂x=−20.cos50πt−10πxAt t = 0, ∂y∂x=−20πcos10πxNow elastic potential energy stored per unit length is proportional to ∂y∂x2∴ u2u1=cos210πx2cos210πx1=cos210π×104×100cos210π×103×100⇒u22=cos2π4cos2π3⇒u2=4 J/m