The extension in a wire obeying Hooke's law is 'x'. The speed of sound in the stretched wire is 'V'. If the…

The extension in a wire obeying Hooke's law is 'x'. The speed of sound in the stretched wire is 'V'. If the extension in the wire is increased to $4 \mathrm{x}$, then the speed of sound in a wire is
  1. $\mathrm{V}$
  2. $2 .5 \mathrm{~V}$
  3. $2 \mathrm{~V}$
  4. $1 .5 \mathrm{~V}$

Solution

$\begin{aligned} \mathrm{V} &=\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \quad \mathrm{T}_{1}=-\mathrm{kx} \quad \mathrm{T}_{2}=-\mathrm{k} 4 \mathrm{x} \\ \therefore \quad \frac{\mathrm{V}_{1}}{\mathrm{~V}_{2}} &=\sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}}=\frac{1}{2} \\ \therefore \quad \mathrm{V}_{2} &=2 \mathrm{~V}_{1} \end{aligned}$ .

Asked in: MHT CET 2020 (16 Oct Shift 1)

Practice more Waves and Sound questions on Aicharya