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

• A. \( 10^6 \, \text{m/s} \)
• B. 125 m/s
• C. 100 m/s
• D. \( 10^5 \, \text{m/s} \)

Hint:

To calculate wave velocity, use the relationship between frequency, wavelength, and velocity: \( v = f \lambda \).

Answer 1

The Correct Option is C

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.