Two ends of a string are tied to two rigid walls and the string is oscillating transeversely with maximum amplitude ‘A’ in the first overtone mode. The total energy of oscillation of the string is 0.32 J. If the same string oscillates with maximum amplitude A/2 in the second overtone mode, its total energy of oscillation will be
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a
0.21 J
b
0.09 J
c
0.27 J
d
0.18 J
answer is D.
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Detailed Solution
If ω0 be the fundamental frequency of the string, then the first overtone frequency is 2ω0 and the second overtone frequency is 3ω0. If ‘A’ be the maximum amplitude and E be the total energy of the string, then total energy ∝ A2ω2E1E=A1A2ω1ω2=122322=916⇒E1=9E/16=9×0.3216J=0.18 J