MHT CET · Physics · Waves and Sound

Air column in two identical tubes is vibrating. Tube A has one end closed and tube B has both ends open. Neglecting end correction, the ratio of the fundamental frequency of air column in tube A to that in tube B is

A \(1: 4\)
B \(4: 1\)
C \(1: 2\)
D \(2: 2\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1: 2\)

Step-by-step Solution

Detailed explanation

The correct option is (C).
Consider the following diagram:

Velocity of a wave \(v\) in a given medium is fixed, as \(v=\lambda \mathrm{f}\), where \(\lambda\) is the wavelength and \(f\) is the frequency.
Therefore,
\(f \propto \frac{1}{\lambda}\)
The ratio of frequencies in case A and case B is given by,
\(\frac{\mathrm{f}_1}{\mathrm{f}_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{2}\)

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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