MHT CET · Physics · Waves and Sound
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
- A \(\frac{\mathrm{Vn}}{\mathrm{x}}\)
- B \(\frac{\mathrm{V}}{\mathrm{nx}}\)
- C \(\frac{\mathrm{Vn}}{2 \mathrm{x}}\)
- D \(\frac{2 x}{V}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{Vn}}{2 \mathrm{x}}\)
Step-by-step Solution
Detailed explanation
Phase difference, \(\phi=\frac{2 \pi \mathrm{x}}{\lambda}\)
Given \(\phi=\mathrm{n} \pi ; \lambda=\frac{\mathrm{V}}{\mathrm{f}}\)
\(\begin{aligned}
& \therefore \mathrm{n} \pi=\frac{2 \pi \mathrm{xf}}{\mathrm{V}} \\
& \therefore \mathrm{f}=\frac{\mathrm{nV}}{2 \mathrm{x}}
\end{aligned}\)
Given \(\phi=\mathrm{n} \pi ; \lambda=\frac{\mathrm{V}}{\mathrm{f}}\)
\(\begin{aligned}
& \therefore \mathrm{n} \pi=\frac{2 \pi \mathrm{xf}}{\mathrm{V}} \\
& \therefore \mathrm{f}=\frac{\mathrm{nV}}{2 \mathrm{x}}
\end{aligned}\)
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