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A transverse wave is produced on a stretched string 0.9 m long and fixed at its ends. Find the speed of the transverse wave, when the string vibrates while emitting second overtone of frequency

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Question

A transverse wave is produced on a stretched string 0.9 m long and fixed at its ends. Find the speed of the transverse wave, when the string vibrates while emitting the second overtone of frequency 324 Hz.

Sum
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Solution

Length of the string L = 0.9 m

For second overtone frequency (or third harmonic mode of vibration) n = 3.

Frequency of nth mode of vibration when the string is fixed at both ends ν = `"nv"/"2L"`​
`∴ 324 = ("3v"​)/(2 xx 0.9)`
 
⟹ v = `(324 xx 0.9 xx 2)/3` ​= 194.4 m/s
We get speed of transverse wave, v = 194.4 m/s.
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2016-2017 (March)

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