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MHT CET · Physics · Waves and Sound

A sound wave of frequency \(160 \mathrm{~Hz}\) has velocity of \(320 \mathrm{~m} / \mathrm{s}\). when it travels through air, the particles having a phase difference of \(90^{\circ}\), are separated by a distance of

  1. A 50 cm
  2. B 1 cm
  3. C 25 cm
  4. D 75 cm
Verified Solution

Answer & Solution

Correct Answer

(A) 50 cm

Step-by-step Solution

Detailed explanation

\(
\begin{aligned}
& \mathrm{f}=160 \mathrm{~Hz}, \mathrm{v}=320 \mathrm{~m} / \mathrm{s} \\
& \lambda=\frac{\mathrm{v}}{\mathrm{f}}=\frac{320}{160}=2 \mathrm{~m}=200 \mathrm{~cm}
\end{aligned}
\)
Phase difference \(\phi=\frac{2 \pi x}{\lambda}\)
\(
\begin{aligned}
& \therefore \mathrm{x}=\frac{\phi \lambda}{2 \pi} \\
& =\frac{\pi}{2} \cdot \frac{\lambda}{2 \pi} \quad\left[\because \phi=\frac{\pi}{2}\right] \\
& =\frac{\lambda}{4}=\frac{200}{4}=50 \mathrm{~cm}
\end{aligned}
\)