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 * 1h/3600s = 20 m/s.
a. Fp = (Vs+Vp)/(Vs-Vt) * Ft =(343+0)/(343-20) * 600 = 637.2 Hz.
b. Fp = (Vs-Vp)/(Vs+Vt) * Ft =
To calculate the frequency heard by the person when the train approaches and recedes away, we need to apply the concept of the Doppler effect. The Doppler effect is the change in frequency of a wave (in this case, sound waves) due to the relative motion between the source of the wave and the observer.
The formula to calculate the frequency heard by the observer can be given as:
f' = f * (v + v₀) / (v - v₀)
Where:
f' = Frequency heard by the observer
f = Frequency of the source (train whistle)
v = Speed of sound in air (approximately 340 m/s)
v₀ = Speed of the observer (person standing still on the platform)
Let's calculate the frequency heard by the person for both scenarios:
(i) When the train approaches:
The speed of the train is 72 km/h. We need to convert it to meters per second (m/s):
Train speed = 72 km/hr = 72 * 1000 m / (60 * 60) s = 20 m/s
Using the given values, we can calculate the frequency heard by the person:
f' (approach) = 600 Hz * (340 m/s + 0 m/s) / (340 m/s - 20 m/s)
(ii) When the train recedes away:
For this scenario, we just need to change the sign of the speed of the observer since the train is moving away:
v₀ (recede) = -0 m/s
Using the given values, we can calculate the frequency heard by the person:
f' (recede) = 600 Hz * (340 m/s + 0 m/s) / (340 m/s - (-20 m/s))
By simply plugging in the values and performing the calculations, we can find the frequencies heard by the person in both cases.
Please note that the calculated result will differ slightly depending on the rounding of values and the specific data used (e.g., exact speed of sound, etc.).