Questions

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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detailed solution

Correct option is B

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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Similar Questions

String of length L whose one end is x = 0 vibrates according to the relations given in column-I. Select matching entries from column-lI including nodes or antinodes at the end points of string.

Column-I		Column-II
(a)	$y = Asin \frac{πx}{L} \sin ωt$	(p)	1 antinode, 2 nodes
(b)	$y = Acos \frac{πx}{L} \sin ωt$	(q)	3 nodes, 2 antinodes
(c)	$y = Asin \frac{2 πx}{L} \sin ωt$	(r)	2 antinodes, 1 node
(d)	$y = Acos \frac{2 πx}{L} \sin ωt$	(s)	3 antinodes, 2 nodes