Question

An obstacle is moving towards the source with velocity \( v \). The sound is reflected from the obstacle. If \( c \) is the speed of sound and \( \lambda \) is the wavelength, then the wavelength of the reflected wave \( \lambda_r \) is

• A. \( \lambda_r = \frac{c - v}{c + v} \lambda \)
• B. \( \lambda_r = \frac{c - v}{c} \lambda \)
• C. \( \lambda_r = \frac{c + v}{c - v} \lambda \)
• D. \( \lambda_r = \frac{c + v}{c} \lambda \)

Hint:

The Doppler effect causes a change in the wavelength of the reflected sound when the obstacle moves. The formula depends on the relative velocity of the source and the obstacle.

Answer 1

The Correct Option is A

Step 1: Doppler Effect for Reflection.
For a moving obstacle reflecting sound, the wavelength of the reflected wave is altered due to the relative motion between the source and the obstacle.
Step 2: Applying the Doppler formula.
The wavelength of the reflected sound is given by the formula: \[ \lambda_r = \frac{c - v}{c + v} \lambda \] where \( c \) is the speed of sound, \( v \) is the velocity of the obstacle, and \( \lambda \) is the wavelength of the incident wave.
Step 3: Conclusion.
The wavelength of the reflected wave is \( \lambda_r = \frac{c - v}{c + v} \lambda \), so the correct answer is (A).