Question

A train is traveling at 30.0 m/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 Hz.
The speed of sound in air should be taken as 344 m/s.
What frequency (f approach) is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it?
What frequency (f recede) is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?

Answer 1

PART A)

the apparent frequency is given by following formula when source and observer is moving towards each other in opposite direction

$f = f_0(\frac{v + v_0}{v - v_s})$

here we know that

$f_0 = 262 Hz$

$v_s = 30 m/s$

$v_0 = 18 m/s$

v = 344 m/s

now from above equation we have

$f = 262(\frac{344 + 18}{344 - 30})$

$f = 302 Hz$

Part b)

the apparent frequency is given by following formula when source and observer is moving away from each other in opposite direction

$f = f_0(\frac{v - v_0}{v + v_s})$

here we know that

$f_0 = 262 Hz$

$v_s = 30 m/s$

$v_0 = 18 m/s$

v = 344 m/s

now from above equation we have

$f = 262(\frac{344 - 18}{344 + 30})$

$f = 228 Hz$