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?
To determine the frequency heard by the train, we can use the formula for the Doppler effect:
f' = f(ct + v) / (ct + vs)
Where:
f' is the frequency heard by the train
f is the frequency heard by the stationary observers (passengers at the station)
c is the speed of sound in air (assumed to be 343 m/s)
t is the time (which doesn't affect the frequency)
v is the velocity of the train (45 m/s)
s is the speed of sound in air (343 m/s)
Plugging in the values, we have:
f' = 373(343 + 45) / (343 - 45)
f' = 373(388) / (298)
f' ≈ 486.94 Hz
Therefore, the frequency heard by the train is approximately 486.94 Hz.
To determine the frequency heard by the train, we can apply the Doppler effect formula:
f' = (v + v₁) / (v - v₀) * f₀
Where:
f' = frequency heard by the train
v = velocity of sound (343 m/s, assuming the speed of sound)
v₁ = velocity of the train (45 m/s)
v₀ = velocity of the observer (0 m/s, since the passengers are still at the station)
f₀ = frequency heard by the observer (373 Hz)
Now, let's substitute the given values into the formula:
f' = (343 + 45) / (343 - 0) * 373
f' = 388 / 343 * 373
f' = 424340 / 343
f' ≈ 1237.76 Hz
Therefore, the frequency heard by the train is approximately 1237.76 Hz.
To determine the frequency heard by the train as it is moving, we need to consider the concept of Doppler effect. The Doppler effect is the change in frequency of a wave, such as sound or light, due to the relative motion between the source of the wave and the observer.
In this case, the train is moving away from the passengers at the station. So, the frequency heard by the train will be lower than the frequency emitted by the horn. We can use the formula for the Doppler effect to find the frequency heard by the train:
f' = f * (v + v₀) / (v + vᵢ)
Where:
f' = Frequency observed by the moving observer (train)
f = Frequency emitted by the source (horn)
v = Speed of sound in air
v₀ = Speed of the observer (train)
vᵢ = Speed of the source (stationary passengers)
First, let's convert the speed of the train from m/s to Hz. The speed of sound in air is approximately 343 m/s.
v₀ = 45 m/s / 343 m/s = 0.131 Hz
Now we can substitute the values into the formula:
f' = 373 Hz * (343 m/s + 0.131 Hz) / (343 m/s + 0 m/s)
f' = 373 Hz * 1.00038
f' ≈ 373 Hz
Therefore, the frequency heard by the train is approximately 373 Hz.