A train is sounding a horn of constant frequency shows down as it nears a station. What change in pitch is heard by a commuter standing in the station?
To determine the change in pitch heard by a commuter standing in the station as the train approaches, we need to understand the concept of the Doppler effect. The Doppler effect is the apparent change in frequency or pitch of a sound wave due to the motion of the source of the sound relative to the observer.
The pitch of a sound is directly related to its frequency. As the train moves closer to the station, the pitch heard by the commuter in the station will increase.
The formula to calculate the change in frequency due to the Doppler effect is:
Δf = (v/v+vO) * f
Where:
Δf is the change in frequency
v is the velocity of sound in air
vO is the velocity of the observer (commuter)
f is the original frequency (frequency of the train horn)
In this case, since the train is slowing down, the velocity of the train (vT) is decreasing. It is important to note that the frequency of the train horn remains constant.
As the train slows down, the velocity (vO) of the observer (commuter) in the station remains constant.
Since the change in frequency is negative when the source (train) is moving towards the observer (commuter), the formula to calculate the change in pitch is:
Δf = -(v/v+vO) * f
By plugging in the appropriate values of the variables, you can calculate the change in pitch (Δf) heard by the commuter in the station.
It's worth mentioning that if the train were to move away from the station, the signs would be reversed, resulting in a decrease in pitch.