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Q.

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)ω2A2sin2⁡πxℓ and dm=mℓdx
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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.