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MHT CET 2025 (20 Apr, Shift 1) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2025 (20 Apr, Shift 1)

Q34MHT CET 2025 · 20 APR · SHIFT 1Medium

Stationary Waves & Vibrating Strings

A wire of length L, diameter ' d ' density of material ' e ' is under tension ' T ', having fundamental frequency of vibration nAn_A. Another wire of length 2 L, tension 2 T, density 2 e and diameter 3 d has fundamental frequency of vibration nBn_B. The ratio nB:nAn_B : n_A is

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Answer: (c)

  1. n=1LdTπe⇒n∝1LdTen = \dfrac{1}{Ld}\sqrt{\dfrac{T}{\pi e}} \Rightarrow n \propto \dfrac{1}{Ld}\sqrt{\dfrac{T}{e}}
  2. nBnA=12×322=16\dfrac{n_B}{n_A} = \dfrac{1}{2\times3}\sqrt{\dfrac{2}{2}} = \dfrac{1}{6}
  3. So the answer is (c) 1:61:6.
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