Question

A car sounding its horn at 480 Hz moves towards a high speed wall of 20 m/s, the frequency of the reflected sound heard by the man sitting in the car will be nearest to:
A. 480 Hz
B. 510 Hz
C. 540 Hz
D. 570 Hz

Answer 1

Hint: In this question we have been asked to calculate the frequency of the sound heard by the man sitting in the car. To solve this question, we will be using Doppler’s effect. It states the relation between the wave and the observer who is moving relative to the wave. In the question the man in the moving car is the observer.

Formula used:
\[f={{f}_{o}}\left( \dfrac{v+{{v}_{o}}}{v-{{v}_{s}}} \right)\]
Where,
f is the frequency of the wave
v is the speed of sound
\[{{v}_{o}}\] is the speed of the observer
\[{{v}_{s}}\] is the speed of the source

Complete answer:
Doppler’s effect tells us the change in wave frequency during the relative motion between a wave source and its observer. If the observer moves away from the source of sound the frequency of the sound heard by the observer will decrease and vice versa.
From the equation of Doppler’s effect
 \[f={{f}_{o}}\left( \dfrac{v+{{v}_{o}}}{v-{{v}_{s}}} \right)\]
Now, it is given that
The frequency of the sound of car’s horn\[{{f}_{o}}=480Hz\]
Observer’s speed \[{{v}_{o}}=20m/s\]
Speed of source\[{{v}_{s}}=20m/s\]
We also the speed of sound \[v=340m/s\]
Therefore, after substituting values in above equation
We get,
\[f=480\left( \dfrac{340+20}{340-20} \right)\]
On solving,
\[f=480\times \dfrac{360}{320}\]
Therefore,
\[f=540Hz\]
So, the frequency heard by the man sitting in the car will be 540 Hz.

So, the correct answer is “Option C”.

Note:
The Doppler effect is mostly used to calculate the speed at which the galaxies or stars are approaching us or moving away from us. The Doppler’s effect is used in hospitals to measure the amount and direction of the blood flow. If there is clot in the flow of blood, the ultrasound will be able to detect the slower blood flow where the clot is located.