Question:
Two trains \(A\) and \(B\) are moving towards each other with speeds \(72\,\text{km h}^{-1}\) and \(36\,\text{km h}^{-1}\) respectively. The train-A whistles at \(640\,\text{Hz}\) frequency. Before the trains meet, frequency of sound heard by a passenger in Train-B is \((v=340\,\text{m s}^{-1})\):
Two trains \(A\) and \(B\) are moving towards each other with speeds \(72\,\text{km h}^{-1}\) and \(36\,\text{km h}^{-1}\) respectively. The train-A whistles at \(640\,\text{Hz}\) frequency. Before the trains meet, frequency of sound heard by a passenger in Train-B is \((v=340\,\text{m s}^{-1})\):
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In Doppler effect, when source and observer move towards each other, apparent frequency increases and is given by
\[
f' = f\left(\frac{v+v_o}{v-v_s}\right)
\]
Updated On: Jun 26, 2026
- \(500\,\text{Hz}\)
- \(600\,\text{Hz}\)
- \(700\,\text{Hz}\)
- \(800\,\text{Hz}\)
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The Correct Option is C
Solution and Explanation
Step 1: Convert speeds into SI units.
Speed of train \(A\) is \[ 72\,\text{km h}^{-1}=72\times \frac{5}{18}=20\,\text{m s}^{-1} \] Speed of train \(B\) is \[ 36\,\text{km h}^{-1}=36\times \frac{5}{18}=10\,\text{m s}^{-1} \] Thus, \[ v_s=20\,\text{m s}^{-1} \] and \[ v_o=10\,\text{m s}^{-1} \]
Step 2: Apply Doppler effect formula.
Since the source and observer are moving towards each other, apparent frequency is \[ f' = f\left(\frac{v+v_o}{v-v_s}\right) \] Here, \[ f=640\,\text{Hz},\quad v=340\,\text{m s}^{-1} \] Therefore, \[ f'=640\left(\frac{340+10}{340-20}\right) \] \[ f'=640\left(\frac{350}{320}\right) \] \[ f'=640\times \frac{35}{32} \] \[ f'=20\times 35 \] \[ f'=700\,\text{Hz} \]
Step 3: Final conclusion.
Therefore, the frequency heard by the passenger in train \(B\) is \[ \boxed{700\,\text{Hz}} \]
Speed of train \(A\) is \[ 72\,\text{km h}^{-1}=72\times \frac{5}{18}=20\,\text{m s}^{-1} \] Speed of train \(B\) is \[ 36\,\text{km h}^{-1}=36\times \frac{5}{18}=10\,\text{m s}^{-1} \] Thus, \[ v_s=20\,\text{m s}^{-1} \] and \[ v_o=10\,\text{m s}^{-1} \]
Step 2: Apply Doppler effect formula.
Since the source and observer are moving towards each other, apparent frequency is \[ f' = f\left(\frac{v+v_o}{v-v_s}\right) \] Here, \[ f=640\,\text{Hz},\quad v=340\,\text{m s}^{-1} \] Therefore, \[ f'=640\left(\frac{340+10}{340-20}\right) \] \[ f'=640\left(\frac{350}{320}\right) \] \[ f'=640\times \frac{35}{32} \] \[ f'=20\times 35 \] \[ f'=700\,\text{Hz} \]
Step 3: Final conclusion.
Therefore, the frequency heard by the passenger in train \(B\) is \[ \boxed{700\,\text{Hz}} \]
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