Question

A source and the observer both are moving towards each other with speed v/10, where v is the speed of sound. If the frequency of the sound emitted by the source is f, then the apparent frequency heard by the observer is,
1. 1.22f
2. 0.82f
3. f
4. 1.11f

Answer 1

Correct Answer - Option 1 : 1.22f

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)

CALCULATION:

Given vo = v m/s, vs = v m/s, and f = frequency of sound

• The apparent frequency is given as,

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

\(⇒ f'=\frac{\left ( v+\frac{v}{10} \right )}{\left ( v-\frac{v}{10} \right )}\times f\)

⇒ f' = 1.22f

• Hence, option 1 is correct.