A progressive wave of frequency $50 \mathrm{~Hz}$ is travelling with velocity $350 \mathrm{~m} / \mathrm{s}$…

A progressive wave of frequency $50 \mathrm{~Hz}$ is travelling with velocity $350 \mathrm{~m} / \mathrm{s}$ through a medium. The change in phase at a given time interval of $0.01 \mathrm{~s}$ is
  1. $\pi \mathrm{rad}$
  2. $\frac{\pi}{4} \mathrm{rad}$
  3. $\frac{\pi}{2} \mathrm{rad}$
  4. $\frac{3 \pi}{2} \mathrm{rad}$

Solution

We know, $\lambda \mathrm{f}=\mathrm{v}$ $\therefore \lambda=\frac{350}{50}=7 \mathrm{~m}$ Path difference $\mathrm{x}=$ Velocity $\times$ time $=350 \times 0.01=3.5 \mathrm{~m}$ Phase change $\frac{2 \pi x}{\lambda}=\frac{2 \pi}{7} \times 3.5=\pi$ radian .

Asked in: MHT CET 2022 (07 Aug Shift 1)

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