MHT CET · Physics · Waves and Sound

A string of mass \(M\) is under a tension \(T\). The length of the string is \(L\). A transverse wave starts at one end of the string., the time required for the disturbance to reach the other end is

A \(\sqrt{\frac{L M}{T}}\)
B \(\sqrt{L M T}\)
C \(\sqrt{\frac{T}{L M}}\)
D \(\sqrt{\frac{L T}{M}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{\frac{L M}{T}}\)

Step-by-step Solution

Detailed explanation

The velocity of transverse wave on a string is given by, \(v=\sqrt{\frac{T}{\mu}}\), where \(T\) is tension and mass per unit length of the string \(\mu=\frac{M}{L}\).
Time required to travel \(L\) distance would be,
\(\frac{L}{v}=L \sqrt{\frac{M}{T L}}=\sqrt{\frac{L M}{T}}\)

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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