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Question

A wire of linear mass density 9×103 kg/m is stretched between two rigid supports under a tension of 360 N. The wire resonates at frequency 210 Hz. The next higher frequency at which the same wire resonates is 280 Hz. The number of loops produced in first case will be
  1. 1
  2. 2
  3. 3
  4. 4


Solution

The correct option is C 3
μ=9×103 kg
T=360 N
Frequency =nv2L
Hence nv2L=210
(n+1)v2L=280
nn+1=212828n=21n+21
3n=21
n=3
In first case
λ=2L3
L=3λ2
A loop is formed in length λ2
Hence no. of loops are 3

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