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Question
A person standing on a road sends a sound signal to the driver of a car going away from him at a speed of 72 km h−1. The signal travelling at 330 m s−1 in air and having a frequency of 1600 Hz gets reflected from the body of the car and returns. Find the frequency of the reflected signal as heard by the person.
Solution
Given:
Velocity of sound in air v = 330 ms−1
Frequency of signal emitted by the source \[n_0\] = 1600 Hz
Velocity of source vs = 72 kmh−1 =\[72 \times \frac{5}{18} = 20 {\text {ms }}^{- 1}\]
As the sound gets reflected, therefore:
Velocity of source ( vs ) = Velocity of observer ( vL )
Velocity of sound heard by the observer is given by :
\[n = \frac{v + v_L}{v - v_s} \times n_0\]
On substituting the values, we get :
\[n = \frac{330 - 20}{330 + 20} \times 1600 = 1417 \text { Hz }\]
The frequency of the reflected signal as heard by the person is 1417 Hz.
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