MHT CET · Physics · Waves and Sound

A transverse wave is travelling on a string with velocity 'V'. The extension in the string is ' \(x^{\prime}\). If the string is extended by \(50 \%\), the speed of the wave along the string
will be nearly (Hooke's law is obeyed)

A \((0.7) \mathrm{V}\)
B \((1.22) \mathrm{V}\)
C \((1.1) \mathrm{V}\)
D \((0.9) V\)

Verified Solution

Answer & Solution

Correct Answer

(B) \((1.22) \mathrm{V}\)

Step-by-step Solution

Detailed explanation

Speed of sound \(\mathrm{V}=\sqrt{\frac{\mathrm{T}}{\mu}}\)
\(\mathrm{V} \propto \sqrt{\mathrm{T}}\)
So \(\frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}=\sqrt{\frac{1.5 \mathrm{x}}{\mathrm{x}}}\)
So \(\quad \mathrm{T} \propto \mathrm{x}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A transverse wave is travelling on a string with velocity 'V'. The extension in the string is ' \(x^{\prime}\). If the string is extended by \(50 \%\), the speed of the wave along the stringwill be nearly (Hooke's law is obeyed)

Step-by-step Solution

A transverse wave is travelling on a string with velocity 'V'. The extension in the string is ' \(x^{\prime}\). If the string is extended by \(50 \%\), the speed of the wave along the string
will be nearly (Hooke's law is obeyed)