Doppler Shift Question A train blows its whistle with freque

Doppler Shift Question

A train blows its whistle with frequency of f=1000 Hz while traveling down a straight track at a speed of 100.00 m/s. You, the observer, are standing at a point that is 100.0 m from the track. Define time t = 0 is the moment when the train is the closest distace to you. Use the speed of sound as 343.0 m/s.

I\'m mostly confused because I think I almost understand it, but not quite. What\'s happening? I\'ve put what answers I got earlier

(a)What frequency do you hear when

i.the train is far away and approaching? I got 872hz

ii.the train is far away and receding? I got 1171 hz

iii.the train passes you (at time t = 0)?

I don\'t understand this. Shouldn\'t it just be the hz, since we don\'t have a doppler effect at this instance? Does distance matter? If so, do I use the spherical sound equation

(b)What frequency do you hear at timet = 10 s and att = 5 s?

Again, I don\'t understand. Given that the train goes 50mps, then at -10s it is 500 m away from the point where you are perpendicular to the track and at -5 s it is 250 m away. We can use pythagorean to find the shortest distance from you to the track, but....

(c)Write an equation for the frequency that you hear as a function of time and sketch or plot this equation

Solution

f = 1000 Hz

u = 100 m/s

distance from track, d = 100 m

c = 343 m/s

a. when the train is approaching

fd = (c/(c - u))f = 1411.52263 Hz

b. when the rrain is receeding

fd = (c/c+u))f = 774.2663 Hz

c. the train passes you

f = 1000 Hz

B. at any time < 0 s the frequency is 1411.522 Hz if the train is approaching