Question

37. A train moving at a speed of 30 ms' approaches a station and sounds a horn of frequency 500 Hz. What is the
apparent frequency of the horn as heard by a man on the platform as the train approaches him. Calculate the
change in frequency as heard by the Man.
Given : Speed of Sound = 340 ms?​

Answer 1

$\displaystyle f = f_\circ \left (\frac{v \pm v_o}{v \pm v_s} \right )$  

Vo --> Velocity of observer

Vs --> velocity of source

v --> Velocity of sound

$\displaystyle f =500 \left (\frac{340 }{ 340 - 30} \right ) = 500 \left (\frac{34 }{ 31} \right ) = 548.38 \text{ Hz}$

Here we have used -ve sign in the denominator because since the train is approaching the observer, the frequency would increase and lesser the denominator, greater the fraction.

Difference in frequency = 548.38 - 500 = 48.38 Hz