TS EAMCET · Physics · Waves and Sound

A sound wave of frequency 210 Hz travels with a speed of \(330 \mathrm{~ms}^{-1}\) along the positive x-axis. Each particle of the wave moves a distance of 10 cm between the two extreme points. The equation of the displacement function (s) of this wave is ( \(x\) in metre, \(t\) in second)

A \(s(x, t)=0.10 \sin [4 x-1320 t] m\)
B \(\mathrm{s}(\mathrm{x}, \mathrm{t})=0.05 \sin [4 \mathrm{x}-1320 \mathrm{t}] \mathrm{m}\)
C \(\mathrm{s}(\mathrm{x}, \mathrm{t})=0.05 \sin [1320 \mathrm{x}-4 \mathrm{t}] \mathrm{m}\)
D \(\mathrm{s}(\mathrm{x}, \mathrm{t})=0.10 \sin [1320 \mathrm{x}-4 \mathrm{t}] \mathrm{m}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mathrm{s}(\mathrm{x}, \mathrm{t})=0.05 \sin [4 \mathrm{x}-1320 \mathrm{t}] \mathrm{m}\)

Step-by-step Solution

Detailed explanation

Amplitude: \( A = \frac{10 \text{ cm}}{2} = \frac{0.10 \text{ m}}{2} = 0.05 \text{ m} \) Angular frequency: \( \omega = 2\pi f = 2\pi (210) \approx 1320 \text{ rad/s} \) Wave number: \( k = \frac{\omega}{v} = \frac{1320 \text{ rad/s}}{330 \text{ m/s}} = 4 \text{ rad/m} \)…

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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