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Question
Two trains are travelling towards each other both at a speed of 90 km h−1. If one of the trains sounds a whistle at 500 Hz, what will be the apparent frequency heard in the other train? Speed of sound in air = 350 m s−1.
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Solution
Given:
Velocity of sound in air v = 350 ms−1
Velocity of source \[v_s\] = 90 km/hour =\[90 \times \frac{5}{18}\]= 25 m/s
Velocity of observer \[v_0\] = 25 m/s
Frequency of whistle \[f_0\] = 500 Hz
Apparent frequency\[\left( f \right)\] heard by the observer in train B is given by:
\[f = \left( \frac{v - v_0}{v - v_s} \right) f_0\]
On substituting the respective values in the above equation, we get:
\[f = \left( \frac{350 + 25}{350 - 25} \right) \times 500 = 577 \text { Hz }\]
The apparent frequency heard in the other train is 577 Hz.
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