You are standing on a train station platform as a train goes by close to you. As the train approaches, you hear the whistle sound at a frequency of f1 = 94 Hz. As the train recedes, you hear the whistle sound at a frequency of f2 = 71 Hz. Take the speed of sound in air to be v = 340 m/s. Part (a). Find an equation for the speed of the sound source. (In this case, it is the speed of the train.)
Part (b). Find the numeric value, in meters per second, for the speed of the train.
Part (c). Find an equation for the frequency of the train whistle that you would hear if the train were not moving.
Part (d). Find the numeric value, in hertz, for the frequency of the train whistle that you would hear if the train were not moving.

Kindly check explanation

Explanation:

Given the following :

As train approaches ; frequency, f1 = 94Hz

As train recedes; frequency, f2 = 71Hz

Speed of sound in air ; v = 340m/s

A) speed of sound source (speed of train) = vs

From doppler effect :

As the train recedes ;

f2 = fs [v / (v + vs)] - - - - (1)

As train approaches :

f1 = fs [v / (v - vs)] (2)

To find vs equate (1) and (2)

fs [v / (v - vs)] = fs [v / (v + vs)]

f1/f2 = v / (v - vs) ÷ v / (v + vs)

f1 / f2 = v / (v - vs) × (v + vs) / v

f1 / f2 = (v + vs) / (v - vs)

Let f1 / f2 = f

f = (v + vs) / (v - vs)

f (v - vs) = v + vs

fv - fvs = v + vs

fv - v = vs + fvs

v(f - 1) = vs(1 + f)

v(f - 1) / (1 + f) = vs

B)

v(f - 1) / (1 + f) = vs

f = f1 / f2 = 94/71 = 1.32 Hz

340(1.324 - 1) / (1 + 1.324) = vs

vs = 340(0.324) / 2.324

vs = 110.16 / 2.324

vs = 47.40 m/s

C.) To calculate fs, frequency of train, substitute vs into our equation.

f2 = fs [v / (v + vs)]

Following our substitikn we obtain:

fs = (2f / (f + 1))f2

D)

fs = (2f / (f + 1))f2

fs = 2(1.324) / (1.324 +1)) × 71

fs = (2.648 / 2.324) × 71

fs = 1.1394148 × 71

fs = 80.898450

fs = 80.90 Hz

80cm/s.

24cm/s.

53.3cm/s.