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A source and a listener are moving towards each other with a speed 1/10th of the speed of sound. if the frequency of the note emitted by the source is f, the frequency of the note heard by the listner will be nearly
  • a)
    1.11 f
  • b)
    1.22 f
  • c)
    f
  • d)
    1.33 f
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A source and a listener are moving towards each other with a speed 1/1...
Solution:

Concept: Doppler's Effect

The apparent change in the frequency of sound due to the relative motion between the source and the listener is called the Doppler effect.

When the source and the listener are moving towards each other, the frequency heard by the listener is given by

f' = f(v + vL) / (v + vS)

where

f = frequency of sound emitted by the source,

f' = frequency of sound heard by the listener,

v = speed of sound in air,

vS = speed of the source,

vL = speed of the listener.

Calculation:

Given,

vS = vL = v/10

f' = f(v + vL) / (v + vS)

f' = f(v + v/10) / (v + v/10)

f' = f(11v/10) / (21v/10)

f' = 11f/21

f' ≈ 1.22f

Hence, option (B) is the correct answer.

Answer: (B) 1.22 f
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