Frequency question?

Question

A person standing at a railway crossing hears a sound of the horn whose frequency is 450Hz, of an approaching train. Assuming the speed of sound is 343m/s

(a). Find the speed of the train. (the real frequency of the horn is 380Hz)

(b). Find the frequency that the person hears when the train leaves him.

(c). Find the frequency that the person hears if the speed of the leaving train is the same as the speed of sound.

Answer 1

The doppler formula is fd = (vm/(vm-vs))*fs.  We're solving for vs (velocity of source).  This formula is for the source moving towards the observer.

450 = (343/(343-vs))*380

450/380 = 343/(343-vs)

1.18 = 343/(343-vs)

(1.18*343) - 1.18vs = 343

404.74 - 1.18 vs = 343

404.74-343 = 1.18 vs

61.74 = 1.18vs

vs = 61.74/1.18

a) vs = 52.32 m/s (a mighty fast moving train.)

b) fd = (343/(353+52))*380

    fd = 329.97 Hz when train is going away.

c) fd = (343/(343+343))*380

    fd = 190 Hz apparent frequency if train goes away at speed of sound.