Sound WavesHard
Question
The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment the displacement of the wire is y1 = A sin 
sin ωt and energy is E1 and in other experiment its displacement is y2 = A sin 
sin 2ωt and energy is E2. Then
sin ωt and energy is E1 and in other experiment its displacement is y2 = A sin sin 2ωt and energy is E2. Then Options
A.E2 = E1
B.E2 = 2E1
C.E2 = 4E1
D.E2 = 16E1
Solution
Energy E ∝ (amplitude)2 (frequency)2
Amplitude (A) is same in both cases, but frequency 2ω in the second case is two times the frequency (ω) in the first case.
Therefore, E2 = 4E1.
Amplitude (A) is same in both cases, but frequency 2ω in the second case is two times the frequency (ω) in the first case.
Therefore, E2 = 4E1.
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