WBJEE · Physics · Waves and Sound
The displacement of a plane progressive wave in a medium, travelling towards positive \(x\)-axis with velocity \(4 \mathrm{~m} / \mathrm{s}\) at \(t=0\) is given by \(y=3 \sin 2 \pi\left(-\frac{x}{3}\right)\). Then the expression for the displacement at a later time \(t=4\) sec will be
- A \(y=3 \sin 2 \pi\left(-\frac{x-16}{3}\right)\)
- B \(y=3 \sin 2 \pi\left(\frac{-x-16}{3}\right)\)
- C \(y=3 \sin 2 \pi\left(\frac{-x-1}{3}\right)\)
- D \(y=3 \sin 2 \pi\left(\frac{-x-1}{3}\right)\)
Answer & Solution
Correct Answer
(A) \(y=3 \sin 2 \pi\left(-\frac{x-16}{3}\right)\)
Step-by-step Solution
Detailed explanation
Hint : Let \(y=3 \sin [\omega t-\mathrm{kx}]\) \(\frac{\text { at } t=0}{y=3 \sin (-k x)}\) \(k=\frac{2 \pi}{3}\) \(v=\frac{\omega}{k}\) \(4=\frac{\omega}{2 \pi / 3} \quad \Rightarrow \quad \omega=\frac{8 \pi}{3}\)…
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