Question

A car is approaching a factory siren that has a frequency of 510 Hz. The speed of sound in air is 340 m/s. If the apparent frequency of the sound as heard by the car driver is 600 Hz, then the speed of the car is:

• A. 60 m/s
• B. 33.3 m/s
• C. 50.5 m/s
• D. 80 m/s

Hint:

For Doppler effect with moving observer and stationary source: \(f' = f (v + v_o)/v\). Solve for \(v_o\) when apparent frequency is given.

Answer 1

The Correct Option is A

Step 1: Doppler formula for moving observer.
f' = f (v + v_o)/v, with stationary source and observer approaching. v = 340 m/s, f = 510 Hz, f' = 600 Hz.

Step 2: Solving for observer velocity.
600 = 510 (340 + v_o)/340 → 600/510 = (340 + v_o)/340 → (600/510)×340 = 340 + v_o → 400 = 340 + v_o → v_o = 60 m/s.

Step 3: Conclusion.
The car approaches the siren at 60 m/s.