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Question

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving at a speed of 20m/s with respect to the ground. If an observer in car A detects a frequency of 2000Hz of the sound coming from car B, what is the natural frequency of the sound source in car B? (speed of sound in air =340m/s)


A

2250Hz

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B

200Hz

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C

2300Hz

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D

2150Hz

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Solution

The correct option is A

2250Hz


Step 1. Given data

Two cars A and B are moving away in opposite direction at speed of 20m/s and speed of sound in are is 340m/s.

We have to find the natural frequency of the sound source in car B.

Step 2. Formula to be used

The Doppler effect is the apparent change in the frequency of a wave motion when there is relative motion between the source of the waves and the observer.

So,

f=(v±vovvs)f0

Here, f0 is the actual frequency of the sound waves, f is observed frequency, v is the speed of the sound waves, v0 is the velocity of the observer and vs is the velocity of the source.

Step 3. Set the values according to the formula.

Let vo be the speed of an observer sitting in car A i.e. it is the speed of car A seen in the above figure.

and
vs be the speed of car B.
So,

v0=vs

=20m/s
Consider v is the speed of sound in air.

Therefore,

v=340m/s
From the given, an observer in car A detects a frequency of 2000Hz of the sound coming from car B,

Therefore, the apparent frequency f=2000Hz
Let us assume that f0 is the natural frequency.
According to the Doppler Effect, the apparent frequency is given as

f=(v±vovvs)f0
Since both cars are moving away from each other, we have,

f=(vvov+vs)f0

Step 4. Find the natural frequency of the sound source in car B.
Substitute the given values in the above equation, we get,

2000=(34020340+20)f0

=(340+2034020)×2000

=2250Hz

Thus, the natural frequency of the sound source in car B is 2250Hz.

Hence, option (A) is the correct answer.


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