Question

When both the source of sound and observer approach each other with a speed equal to 10% of the speed of sound, then the percentage change in frequency heard by the observer is nearly

• A. 33.3%
• B. 12.2%
• C. 22.2%
• D. 11.1%

Hint:

When both source and observer move towards each other, Doppler effect frequency shift is calculated by \(\frac{v + v_o}{v - v_s}\).

Answer 1

The Correct Option is C

Using Doppler effect formula for both source and observer moving towards each other with speed \(v_s = v_o = 0.1v\), where \(v\) is speed of sound: \[ f' = f \times \frac{v + v_o}{v - v_s} = f \times \frac{v + 0.1v}{v - 0.1v} = f \times \frac{1.1v}{0.9v} = 1.222 f \] Percentage change in frequency: \[ (1.222 - 1) \times 100 = 22.2% \]