If the speed of longitudinal waves is equal to $10$ times the speed of the transverse waves in a stretched…

If the speed of longitudinal waves is equal to $10$ times the speed of the transverse waves in a stretched wire of material which has modulus of elasticity $E$, then the stress in the wire is
  1. $10E$
  2. $100E$
  3. $\frac{E}{10}$
  4. $\frac{E}{100}$

Solution

According to the question, $\sqrt{\frac{E}{\rho}} = 10 \sqrt{\frac{T}{\mu}}$ $\Rightarrow 100 \left(\frac{T}{\mu}\right) = \frac{E}{\rho} \Rightarrow \frac{T}{s} = \frac{E \mu}{100 \rho s}$ Since, $\rho s = \mu$ $\therefore \text{Stress} = \frac{T}{s} = \frac{E}{100}$

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