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Question

A string with a mass density of 4×103 kg/m is under a tension of 360 N and is fixed at both ends. One of its resonance frequencies is 375 Hz. The next higher resonance frequency is 450 Hz. If the mass of the string is represented by x×103 kg, find x 


Solution

Given that,
Mass density of the string, μ=4×103 kg/m
Tension, T=360 N
Frequency of first resonance, f1=375 Hz
Next higher frequency, f2=450 Hz
We can write,
f1=375=n2lTμ and f2=450=n+12lTμ
where n is number of segments vibrating.
f2f1=450375=n+1nn=5
So, length of string l=n2×f1Tμ=52×3753604×103=2 m
Mass of wire =(μ)(l)=(4×103×2)=8×103 kg

Physics

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