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MHT CET · Physics · Waves and Sound

A sonometer wire under suitable tension having specific gravity ' \(\varrho^{\prime}\), vibrates with frequency 'n' in air. If the load is completely immersed in water the frequency of vibration of wire will become

  1. A \(\left[\frac{0-1}{n \varrho}\right]^{\frac{1}{2}}\)
  2. B \(n\left[\frac{\varrho}{0-1}\right]^{\frac{1}{2}}\)
  3. C \(\left[\frac{n \varrho}{0-1}\right]^{\frac{1}{2}}\)
  4. D \(n\left[\frac{0-1}{\varrho}\right]^{\frac{1}{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(n\left[\frac{0-1}{\varrho}\right]^{\frac{1}{2}}\)

Step-by-step Solution

Detailed explanation

\((\mathrm{C})\)
\(\mathrm{T}_{1}=\mathrm{mg}=\mathrm{v} \rho \mathrm{g}\)
\(\mathrm{T}_{2}=\mathrm{v}(\rho-\sigma) \mathrm{g} \quad \sigma=1\) for water
\(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\mathrm{vpg}}{\mathrm{v}(\rho-1) \mathrm{g}}=\frac{\rho}{\rho-1}\)
\(\therefore \frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\sqrt{\frac{\rho}{\rho-1}} \quad \therefore \mathrm{n}_{2}=\mathrm{n}_{1} \sqrt{\frac{\rho-1}{\rho}}\)