Question

Two trains A and B are moving towards each other with speeds 72 kmh$^{-1}$ and 36 kmh$^{-1}$ respectively. The train-A whistles at 640 Hz frequency. Before the trains meet, frequency of sound heard by a passenger in Train-B is (Speed of sound in air = 340 ms$^{-1}$)

• A. 500 Hz
• B. 600 Hz
• C. 700 Hz
• D. 800 Hz

Hint:

Convert all velocities to the same unit (m/s) before applying the Doppler formula.
For approaching source and observer, use \( f' = f \left( \frac{v + v_o}{v - v_s} \right) \).
Higher frequency is heard when source and observer are approaching each other.

Answer 1

The Correct Option is C

Use the Doppler effect formula for a moving source and observer: \[ f' = f \left( \frac{v + v_o}{v - v_s} \right) \] Convert speeds: \[ v_s = 72\,\text{km/h} = 20\,\text{m/s}, \quad v_o = 36\,\text{km/h} = 10\,\text{m/s}, \quad v = 340\,\text{m/s} \] \[ f' = 640 \left( \frac{340 + 10}{340 - 20} \right) = 640 \left( \frac{350}{320} \right) = 700\ \text{Hz} \]