A train moving with speed 72 km h−1 emits a whistle of frequency 600 Hz. A
person is standing stationary on the platform. Calculate the frequency heard by the
person if the train (i) approaches and (ii) recedes away from the listener.
Vt = 72,000m/h = 72,000m/3600s = 20 m/s.
1. Fp = (Vs+Vp)/(Vs-Vt) * Ft.
Fp = (343+0)/(343-20) * 600 = 637 Hz.
2. Fp = (343+0)/(343+20) * 600 = 567 Hz.
To calculate the frequency heard by the person in both scenarios, you need to consider the Doppler effect. The Doppler effect is the change in frequency of a wave as a source of the wave moves relative to an observer.
The formula to calculate the frequency observed due to the Doppler effect is as follows:
1. When the source is approaching the listener:
f' = (v + v0) / (v - vs) * f
Here,
f' = observed frequency
f = actual frequency emitted by the source
v = velocity of the sound in the medium (approximately 343 m/s)
v0 = velocity of the listener (0 m/s, as the person is stationary)
vs = velocity of the source (convert the train speed to m/s, i.e., 72 km/h * (1000 m/km) / (3600 s/h))
2. When the source is receding away from the listener:
f' = (v - v0) / (v + vs) * f
All other variables have the same values as in the previous scenario.
Now, let's calculate the frequencies for both cases:
(i) When the train is approaching the listener:
v = 343 m/s
v0 = 0 m/s
vs = 72 km/h * (1000 m/km) / (3600 s/h) = 20 m/s
f = 600 Hz
Plugging these values into the formula:
f' = (343 + 0) / (343 - 20) * 600
f' = 3636 Hz
Therefore, the frequency heard by the person when the train approaches is 3636 Hz.
(ii) When the train recedes away from the listener:
v = 343 m/s
v0 = 0 m/s
vs = -20 m/s (negative sign because the train is moving away)
f = 600 Hz
Plugging these values into the formula:
f' = (343 - 0) / (343 + (-20)) * 600
f' = 514 Hz
Therefore, the frequency heard by the person when the train recedes away is 514 Hz.