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An observer moves towards a stationary source of sound with a speed l/5th of the speed of sound. The wavelength and frequency of the source emitted by any source be λ, and  f respectively. The apparent frequency and wavelength recorded by the observer are respectively -
  • a)
    0.8f, 0.8λ  
  • b)
    1.2f, l.2λ
  • c)
    1.2f, λ    
  • d)
    f, 1.2X
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
An observer moves towards a stationary sourceof sound with a speed l/5...

wavelength remains constant (unchanged) in this case.
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Most Upvoted Answer
An observer moves towards a stationary sourceof sound with a speed l/5...
Let's assume the speed of sound is "v" and the wavelength of the source emitted by any source is "λ".

Since the observer is moving towards the stationary source with a speed of "v/5", the relative velocity between the observer and the source is (v - v/5) = (4v/5).

The formula for the Doppler effect in sound is given by:

f' = (v + Vo) / (v + Vs) * f

where:
f' = frequency observed by the observer
f = frequency emitted by the source
Vo = velocity of the observer
Vs = velocity of the source

In this case, the observer is moving towards the source, so Vo = (4v/5) and Vs = 0 (since the source is stationary).

Plugging in the known values into the formula, we get:

f' = (v + 4v/5) / (v + 0) * f
f' = (5v/5 + 4v/5) / (v + 0) * f
f' = (9v/5) / v * f
f' = (9/5) * f

So, the frequency observed by the observer is (9/5) times the frequency emitted by the source.

Now, let's calculate the wavelength observed by the observer.

The formula for calculating wavelength is given by:

λ' = λ * (v + Vo) / (v + Vs)

Plugging in the known values:

λ' = λ * (v + 4v/5) / (v + 0)
λ' = λ * (9v/5) / v
λ' = (9/5) * λ

So, the wavelength observed by the observer is also (9/5) times the wavelength emitted by the source.

In summary, the wavelength and frequency of the source emitted by any source will both be multiplied by a factor of 9/5 when observed by an observer moving towards the stationary source with a speed of v/5.
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An observer moves towards a stationary sourceof sound with a speed l/5th of the speed of sound. The wavelength and frequency of thesource emitted by any source be λ, and f respectively. The apparent frequency and wavelength recorded by the observer arerespectively -a)0.8f, 0.8λb)1.2f, l.2λc)1.2f, λ d)f, 1.2XCorrect answer is option 'C'. Can you explain this answer?
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