Question

A stationary police car sounds a siren with a frequency of 990 Hz. If the speed of sound is 330 m/s, an observer, driving towards the car with a speed of 33 m/s, will hear a frequency of

• A. 891 Hz
• B. 900 Hz
• C. 1089 Hz
• D. 1100 Hz

Hint:

When observer moves towards a stationary source: \(f' = f\dfrac{v + v_o}{v}\) (frequency increases). When moving away: \(f' = f\dfrac{v - v_o}{v}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Doppler effect with stationary source and moving observer: \(f' = f\dfrac{v + v_o}{v}\).
Step 2: Detailed Explanation:
\[ f' = 990 \times \frac{330 + 33}{330} = 990 \times \frac{363}{330} = 990 \times 1.1 = 1089 \text{ Hz} \]
Step 3: Final Answer:
Frequency heard \(= \mathbf{1089}\) Hz.