Question:
Two points separated by \(6\) cm on a string has phase difference of \(60^{\circ }\). If frequency of oscillation is \(500\) Hz, the velocity of the wave in \(\frac{m}{s}\) is
Two points separated by \(6\) cm on a string has phase difference of \(60^{\circ }\). If frequency of oscillation is \(500\) Hz, the velocity of the wave in \(\frac{m}{s}\) is
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Convert the phase difference to path difference, find the wavelength, then use v equal to f times lambda.
Updated On: Nov 12, 2026
- \(200\)
- \(180\)
- \(100\)
- \(80\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Phase difference and path difference are related by \(\Delta\phi=\dfrac{2\pi}{\lambda}\Delta x\).
Step 2: Wavelength
\(60^{\circ}=\dfrac{\pi}{3}\), so \(\dfrac{\pi}{3}=\dfrac{2\pi}{\lambda}\times6\) cm.
Hence \(\lambda=36\) cm \(=0.36\) m.
Step 3: Speed
\(v=f\lambda=500\times0.36=180\) m/s.
Step 4: Compare the options
This is option (B).
Final Answer:
The wave velocity is 180 m/s. \[ \boxed{\text{(B) }180} \]
Phase difference and path difference are related by \(\Delta\phi=\dfrac{2\pi}{\lambda}\Delta x\).
Step 2: Wavelength
\(60^{\circ}=\dfrac{\pi}{3}\), so \(\dfrac{\pi}{3}=\dfrac{2\pi}{\lambda}\times6\) cm.
Hence \(\lambda=36\) cm \(=0.36\) m.
Step 3: Speed
\(v=f\lambda=500\times0.36=180\) m/s.
Step 4: Compare the options
This is option (B).
Final Answer:
The wave velocity is 180 m/s. \[ \boxed{\text{(B) }180} \]
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