Question

A source emitting a sound of frequency 250 Hz moves towards an observer with a velocity v. If the observer also moves away from the source with the same speed v, the apparent frequency heard by the observer is:
1. 125 Hz
2. 500 Hz
3. 250 Hz
4. None of these

Answer 1

Correct Answer - Option 3 : 250 Hz

CONCEPT:

Doppler effect in physics is defined as the increase (or decrease) in the frequency of sound, light, or other waves as the source and the observer move towards (or away from) each other.

• Waves emitted by a source traveling towards an observer gets compressed. In contrast, waves emitted by a source traveling away from an observer get stretched out.
• Doppler Effect (Doppler Shift) was first proposed by Christian Johann Doppler in 1842.

Doppler effect formula: When the source and the observer moving towards each other

​\(⇒ f'=\frac{(v+ v_{o})}{(v- v_{s})}× f\)

Where f' = apparent frequency(Hz), f = actual frequency(Hz), v = velocity of the sound wave(m/s), vo = velocity of the observer(m/s), and vs = velocity of the sound(m/s)

EXPLANATION:

• In this situation, the source and the observer both are moving in the same direction with the same speed, so their relative velocity is zero.
• Since the relative velocity between the source and the observer is zero, so there will be no doppler effect.
• So the apparent frequency will be the same as that of the original frequency.
• The apparent frequency heard by the observer is 250 Hz. Hence option 3 is correct.