Published by:
CGP EDU Academic Team
Published on: September 11, 2026
The source producing sound and an observer both are moving along the direction of propagation of sound waves. If the respective velocities of sound, source and an observer are v, $v_s$ and $v_o$ , then the apparent frequency heard by the observer will be (n = frequency of sound)
(a) $\frac{n(v+v_o)}{v-v_o}$ (b) $\frac{n(v-v_o)}{v-v_s}$ (c) $\frac{n(v-v_o)}{v+v_s}$ (d) $\frac{n(v+v_o)}{v+v_s}$
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Understanding the Doppler Effect
The Doppler Effect describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. When both the source and the observer are moving towards each other, the frequency increases.
Step 2: Setting Up Variables
Let:
- v = speed of sound
- vs = speed of the source
- vo = speed of the observer
- n = frequency of the sound emitted by the source.
Step 3: Applying the Doppler Effect Formula
When both the source and observer are moving towards each other, the formula for the apparent frequency (n') is given by:
$$ n' = n \frac{(v + v_o)}{(v - v_s)} $$
This takes into consideration the relative velocities of the source and observer with respect to the medium (air in this case).
Step 4: Identifying the Correct Option
From the provided options, we can see that option (a) matches the formula derived above:
$$ n' = n \frac{(v + v_o)}{(v - v_s)} $$
Therefore, the correct answer is: A.
The Doppler Effect describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. When both the source and the observer are moving towards each other, the frequency increases.
Step 2: Setting Up Variables
Let:
- v = speed of sound
- vs = speed of the source
- vo = speed of the observer
- n = frequency of the sound emitted by the source.
Step 3: Applying the Doppler Effect Formula
When both the source and observer are moving towards each other, the formula for the apparent frequency (n') is given by:
$$ n' = n \frac{(v + v_o)}{(v - v_s)} $$
This takes into consideration the relative velocities of the source and observer with respect to the medium (air in this case).
Step 4: Identifying the Correct Option
From the provided options, we can see that option (a) matches the formula derived above:
$$ n' = n \frac{(v + v_o)}{(v - v_s)} $$
Therefore, the correct answer is: A.
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