Question

A and B are two points of a string, in which a standing wave of wavelength \( \lambda \) is set up. If the distance between the points A and B is \( \frac{3\lambda}{4} \), then the phase difference between A and B is:

• A. \( \frac{\pi}{3} \)
• B. \( \frac{3\pi}{4} \)
• C. \( \frac{3\pi}{2} \)
• D. \( \mathbf{\pi} \)

Hint:

- The phase difference between two points in a wave is given by \( \Delta \phi = \frac{2\pi}{\lambda} \times d \). - For standing waves, the phase difference varies between \( 0 \) and \( \pi \). - Always check if phase values exceed \( \pi \) in standing waves and adjust accordingly.

Answer 1

The Correct Option is D

Step 1: Understanding the Phase Difference Formula For a standing wave, the phase difference \( \Delta \phi \) between two points separated by a distance \( d \) is given by: \[ \Delta \phi = \frac{2\pi}{\lambda} \times d \] Step 2: Substituting Given Values Given, \( d = \frac{3\lambda}{4} \), substituting in the equation: \[ \Delta \phi = \frac{2\pi}{\lambda} \times \frac{3\lambda}{4} \] Step 3: Simplifying the Expression \[ \Delta \phi = \frac{6\pi}{4} = \frac{3\pi}{2} \] Step 4: Adjusting for Phase Difference in a Standing Wave Since phase difference in a standing wave can only vary between \( 0 \) and \( \pi \), we take: \[ \Delta \phi = \pi \] Step 5: Verifying the Correct Option Comparing with the given options, the correct answer is: \[ \mathbf{\pi} \]