A string of mass m is fixed at both ends. The fundamental tone oscillation are excited in the string with angular frequency ω and maximum displacement amplitude A. Find the total energy contained in the string.
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a
12mω2A2
b
14mω2A2
c
16mω2A2
d
18mω2A2
answer is B.
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Detailed Solution
y=Asin(kx)cos(ωt)k=2πλ=πℓℓ→ length of sting U=∫x=ℓ dU=∫x=012 (dm)ω2A2sin2πxℓ and dm=mℓdx