Question:
A source of sound emits sound waves at frequency \(f_0\). It is moving towards an observer with fixed speed \(v_s\) (\(v_s \lt v\), where v is the speed of sound in air). If the observer were to move towards the source with speed \(v_0\), one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as \(v_0\) is changed.
The variation of f with \(v_0\) is given correctly by :
A source of sound emits sound waves at frequency \(f_0\). It is moving towards an observer with fixed speed \(v_s\) (\(v_s \lt v\), where v is the speed of sound in air). If the observer were to move towards the source with speed \(v_0\), one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as \(v_0\) is changed.
The variation of f with \(v_0\) is given correctly by :
The variation of f with \(v_0\) is given correctly by :
Show Hint
Write the Doppler formula f = f0 (v+v0)/(v-vs) and treat it as a straight line in v0.
Updated On: Nov 11, 2026
- graph A with slope \(=\frac{f_0}{(v-v_s)}\)
- graph A with slope \(=\frac{f_0}{(v+v_s)}\)
- graph B with slope \(=\frac{f_0}{(v-v_s)}\)
- graph B with slope \(=\frac{f_0}{(v+v_s)}\)
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The Correct Option is A
Solution and Explanation
Source approaching, observer approaching: \(f=f_0\,\frac{v+v_0}{v-v_s}=\frac{f_0 v}{v-v_s}+\frac{f_0}{v-v_s}\,v_0\).
This is linear in \(v_0\) with positive intercept \(\frac{f_0v}{v-v_s}\) and slope \(\frac{f_0}{v-v_s}\), which is graph A (f versus \(v_0\)). Graph B (f versus \(1/v_0\)) would not be a straight line.
Answer: (1) graph A with slope \(\frac{f_0}{v-v_s}\)
This is linear in \(v_0\) with positive intercept \(\frac{f_0v}{v-v_s}\) and slope \(\frac{f_0}{v-v_s}\), which is graph A (f versus \(v_0\)). Graph B (f versus \(1/v_0\)) would not be a straight line.
Answer: (1) graph A with slope \(\frac{f_0}{v-v_s}\)
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