Question:
In a medium in which a transverse progressive wave is travelling, the phase difference between two points with a separation of 1.25 cm is $ \frac{\pi}{4} $. If the frequency of the wave is 1000 Hz, the wave velocity will be
In a medium in which a transverse progressive wave is travelling, the phase difference between two points with a separation of 1.25 cm is $ \frac{\pi}{4} $. If the frequency of the wave is 1000 Hz, the wave velocity will be
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To calculate wave velocity, use the relationship between frequency, wavelength, and velocity: \( v = f \lambda \).
Updated On: Mar 16, 2026
- \( 10^6 \, \text{m/s} \)
- 125 m/s
- 100 m/s
- \( 10^5 \, \text{m/s} \)
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The Correct Option is C
Solution and Explanation
The phase difference between two points is related to the wave velocity by the equation:
\[
\Delta \phi = \frac{2 \pi \Delta x}{\lambda}
\]
where \( \Delta \phi = \frac{\pi}{4} \), and the separation \( \Delta x = 1.25 \, \text{cm} = 0.0125 \, \text{m} \).
The wavelength \( \lambda \) can be found using the wave velocity formula: \[ v = f \lambda \]
Thus, the wave velocity is calculated to be 100 m/s.
The wavelength \( \lambda \) can be found using the wave velocity formula: \[ v = f \lambda \]
Thus, the wave velocity is calculated to be 100 m/s.
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