Question

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be _________ Hz.

Hint:

Mnemonic: For frequency, "Observer on Top, Source at Bottom". If distance increases, frequency decreases; so subtract from the top and add to the bottom.

Answer 1

Correct Answer: 2025

Step 1: Understanding the Concept:
The Doppler Effect explains the change in observed frequency due to the relative motion between the source and the observer. When they move away from each other, the observed frequency is lower than the actual frequency.
Step 2: Key Formula or Approach:
General Doppler formula: \(f' = f \left( \frac{v \pm v_d}{v \mp v_s} \right)\).
When both move away: \(f' = f \left( \frac{v - v_d}{v + v_s} \right)\).
Step 3: Detailed Explanation:
Given:
Apparent frequency \(f' = 1800 \text{ Hz}\).
Speed of sound \(v = 340 \text{ m/s}\).
Speed of source \(v_s = 20 \text{ m/s}\).
Speed of detector \(v_d = 20 \text{ m/s}\).

Using the formula for moving away:
\[ 1800 = f \left( \frac{340 - 20}{340 + 20} \right) \]
\[ 1800 = f \left( \frac{320}{360} \right) \]
\[ 1800 = f \left( \frac{8}{9} \right) \]
\[ f = 1800 \times \frac{9}{8} \]
\[ f = 225 \times 9 = 2025 \text{ Hz} \]
Step 4: Final Answer:
The original frequency of the source is 2025 Hz.