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Question

A one-metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

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Solution

Given:
Length of the stretched string (L) = 1.00 m
Mass of the string =40 g
String is attached to the tuning fork that vibrates at the frequency (f) = 128 Hz
Linear mass density (m) =40×10-3 kg/m
No. of loops formed, (n) = 4
L=nλ2λ=2Ln=2×14λ=0.5 mWave speed (v)=fλ=128×0.5v=64 m/s

We know: v=TmT=ν2m =642×40×10-3 =163.84164 N
Hence, the tension in the string if it is to vibrate in four loops is 164 N.

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