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 ^$(f)$ heard by the observer in train B is given by:

$f = (\frac{v - v_{0}}{v - v_{s}}) f_{0}$

On substituting the respective values in the above equation, we get:

$f = (\frac{350 + 25}{350 - 25}) \times 500 = 577 Hz$

The apparent frequency heard in the other train is 577 Hz.

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