MHT CET · Physics · Waves and Sound
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
- A \(\mathrm{V}\)
- B \(2 .5 \mathrm{~V}\)
- C \(2 \mathrm{~V}\)
- D \(1 .5 \mathrm{~V}\)
Answer & Solution
Correct Answer
(C) \(2 \mathrm{~V}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \mathrm{V} &=\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \quad \mathrm{T}_{1}=-\mathrm{kx} \quad \mathrm{T}_{2}=-\mathrm{k} 4 \mathrm{x} \\ \therefore \quad \frac{\mathrm{V}_{1}}{\mathrm{~V}_{2}} &=\sqrt{\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}}=\frac{1}{2} \\ \therefore \quad \mathrm{V}_{2} &=2 \mathrm{~V}_{1} \end{aligned}\)
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