Velocity of sound waves in air is ' $\mathrm{V}$ ' $\mathrm{m} / \mathrm{s}$. For a particular sound wave in…

Velocity of sound waves in air is ' $\mathrm{V}$ ' $\mathrm{m} / \mathrm{s}$. For a particular sound wave in air, path difference of ' $x$ ' $\mathrm{cm}$ is equivalent to phase difference $n \pi$. The frequency of this wave is
  1. $\frac{\mathrm{Vn}}{\mathrm{x}}$
  2. $\frac{\mathrm{V}}{\mathrm{nx}}$
  3. $\frac{\mathrm{Vn}}{2 \mathrm{x}}$
  4. $\frac{2 x}{V}$

Solution

Phase difference, $\phi=\frac{2 \pi \mathrm{x}}{\lambda}$ Given $\phi=\mathrm{n} \pi ; \lambda=\frac{\mathrm{V}}{\mathrm{f}}$ $\begin{aligned} & \therefore \mathrm{n} \pi=\frac{2 \pi \mathrm{xf}}{\mathrm{V}} \\ & \therefore \mathrm{f}=\frac{\mathrm{nV}}{2 \mathrm{x}} \end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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