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A string fixed at both ends is vibrating in the lowest mode of vibration for which a point at quarter of its length from one end is a point of maximum displacement. The frequency of vibration in this mode is 100 Hz. The frequency emitted when it vibrates in the next mode, such that this point is again a point of maximum displacement is η×100 Hz, where the value of η is

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Solution

fn=nv2L

(n = 2) f1=2v2L


(n = 6) f2=6v2L
f2f1=6v2L2v2L=3 f2=3f1=3×100=300 Hz
η=3

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