A train is moving past a crossing where cars are waiting for it to pass. While waiting, the driver of the lead car becomes sleepy and rests his head on the steering wheel, unintentionally activating the car's horn. A passenger in the back of the train hears the horn's sound at a frequency of 433 Hz and a passenger in the front hears it at 411 Hz.
Find the train's speed and the horn's frequency, assuming the sound travels along the tracks. Take the speed of sound to be 343 m/s.

a) 8.94 m/s

b) 422 Hz

Explanation:

The horns frequency F(g) is given by

F(g) = (411 +433) / 2

F(g) = 844 / 2

F(g) = 422 Hz

The speed is the train is given by

F(r) = [V(s) + V(r)] / [V(s) + V(g)] * F(g)

Where,

F(r) = 433 Hz

F(g) = 422 Hz

V(s) = 343 m/s

V(g) = 0 m/s

V(r) = velocity of train

433 = [V(s) + V(r)] / [V(s) + V(g)] * F(g)

[343 + V(r)] / [343 + 0] * 422 = 433

[343 + V(r)] * 422 = 148519

343 + V(r) = 351.94

V(r) = 351.94 - 343

V(r) = 8.94 m/s

Therefore, the Velocity of receiver(train) is 8.94 m/s