As a train pulls out of the station going 45 m/s it blasts its horn, what is the frequency heard by the train if the passengers still at the station are hearing 373 Hz?
gr 11 physics
To determine the frequency heard by the train, we need to take into account the Doppler effect. The Doppler effect is the change in frequency of a wave (in this case, sound) perceived by an observer when there is relative motion between the source of the sound and the observer.
The formula for the Doppler effect with sound is given by:
f' = f * (v + Vr) / (v + Vs)
Where:
f' = frequency heard by the observer
f = frequency of the source (in this case, the horn)
v = speed of sound in air (approximately 343 m/s)
Vr = speed of the receiver (in this case, the train)
Vs = speed of the source (in this case, the speed of the train)
We know that the frequency heard by the passengers at the station (f') is 373 Hz and the speed of sound in air (v) is approximately 343 m/s.
Let's rearrange the equation to solve for the speed of the train (Vr):
Vr = (f' - f * (v + Vs)) / f
Substituting the given values:
Vr = (373 - 343 * (343 + 45)) / 343
Calculating the result:
Vr = (373 - 343 * 388) / 343
Vr = (373 - 133484) / 343
Vr = -133111 / 343
Vr ≈ -388.2 m/s
The negative sign indicates that the train is moving away from the stationary passengers at the station.
Therefore, the frequency heard by the train is lower than the frequency heard by the passengers at the station.
To determine the frequency heard by the train, we can use the Doppler effect equation:
f' = (v + vo) / (v + vs) * f
Where:
f' = frequency heard by the train
v = speed of sound in air (approximately 343 m/s)
vo = velocity of the observer (train) = 45 m/s (since the train is moving)
vs = velocity of the source (stationary passengers) = 0 m/s (since they are not moving)
f = frequency heard by the stationary passengers = 373 Hz
Plugging in the values:
f' = (343 + 45) / (343 + 0) * 373
f' = 388 / 343 * 373
f' ≈ 423.78 Hz
Therefore, the frequency heard by the train is approximately 423.78 Hz.
To determine the frequency heard by the train as it pulls out of the station, we can use the concept of the Doppler effect. The Doppler effect describes how the frequency of a sound wave changes when there is relative motion between the source of the sound and the observer.
In this scenario, the train is the source of the sound (the horn), and the stationary passengers at the station are the observers. The train is moving away from the stationary observers, resulting in a change in the frequency of the sound wave heard by the observers.
The formula for the apparent frequency (f') heard by the observer is given by:
f' = f * (v + v_r) / (v + v_s)
Where:
f is the actual frequency of the source (horn), which is 373 Hz.
v is the speed of sound, which is approximately 343 m/s.
v_r is the velocity of the observers (stationary passengers), which is 0 m/s as they are not moving.
v_s is the velocity of the source (the train), which is 45 m/s.
Substituting the given values into the formula, we get:
f' = 373 * (343 + 0) / (343 + 45)
≈ 373 * 343 / 388
≈ 330.20 Hz
Therefore, the frequency heard by the train as it pulls out of the station is approximately 330.20 Hz.