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# A stationary source produces a note of frequency 350 Hz. An observer in a car moving towards the sources measures frequency of 370 Hz. Find Speed of a car.

Last updated date: 10th Aug 2024
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Hint: In this question we will use the relation between the frequency and the velocity; next we will substitute the given values in the equation. This will give us the required result. We will also discuss the basics of speed and frequency for our better understanding.
Formula used:
$na = n(v + {v_0}/v)$
$na = n(v - {v_0}/v)$

We have equation for frequency, when the observer in the car moves towards the stationary source, given by:
$na = n(v + {v_0}/v)$
Substituting the given values in above equation, we get:
\eqalign{& 370 = 350(340 + {v_0}/340) \cr & \Rightarrow 359.42 = 340 + {v_0} \cr & \Rightarrow {v_0} = 19.43m/s \cr}
Now, when the car moves towards the stationary source then our equation becomes:
$na = n(v - {v_0}/v)$
Here, substituting the given values in above equation, we get:
\eqalign{& na = 350(340 - 20/340) \cr & \Rightarrow na = 35/34 \times 320 \cr & \therefore na = 329.41Hz \cr}
Therefore, we get the required answers, i.e., the speed of the car is 19.43m/s and frequency of the sound measured by the observer in the car is given by 329.41 Hz.