Apparent change in wavelength of sound waves is $2.5 c m$ when the source of sound is approaching stationary listener with a velocity $17 m / s$ . Apparent decrease in the frequency of source when observer recedes from the same source at rest with a velocity of $25 m / s$ is: (Velocity of sound $= 340 m / s$ )

20 H z

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25 H z

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40 H z

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50 H z

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Solution

The correct option is D $50 H z$
Given: Change in wavelength, $Δ λ = 2.5 c m = 0.025 m$ ,
Velocity of source, $v_{s} = 17 m / s$ ,
Velocity of sound, $v = 340 m / s$

We have apparent change in frequency when source is approaching the stationary observer.

$Δ λ = λ . v_{s} / v$

$λ = Δ λ . v / v_{s} = 0.025 \times 340 / 17 = 0.5 m$

Now when observer recedes from the stationary source with velocity, $v_{o} = 25 m / s$

Apparent frequency is given by: $Δ f = f . v_{o} / v = \frac{v}{λ} . \frac{v_{o}}{v}$

$Δ f = v_{o} / λ = 25 / 0.5 = 50 H z$

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Apparent change in wavelength of sound waves is 2.5cm when the source of sound is approaching stationary listener with a velocity 17m/s. Apparent decrease in the frequency of source when observer recedes from the same source at rest with a velocity of 25m/s is: (Velocity of sound =340m/s)