A person standing close to a railroad crossing hears the whistle of an approaching train. He notes that the pitch of the whistle drops as the train passes by and moves away from the crossing. The frequency of the distant approaching whistle is 540 Hz; it drops to 470 Hz after the train is well past the crossing. What is the speed of the train? Use 340 m/s for the speed of sound in air.

Question

A person standing close to a railroad crossing hears the whistle of an approaching train. He notes that the pitch of the whistle drops as the train passes by and moves away from the crossing. The frequency of the distant approaching whistle is 540 Hz; it drops to 470 Hz after the train is well past the crossing. What is the speed of the train? Use 340 m/s for the speed of sound in air.

Answer 1

F = ((V-Vr) / (V+Vs))*Fs = 470.

((340-0)/(340+Vs))*540 = 470
((340)/(340+Vs))*540 = 470
183600/(340+Vs) = 470
470(340+Vs) = 183600
Divide both sides by 470:
340+Vs = 390.64
Vs = 390.64-340 = 50.64 m/s. = Velocity
of the source or train.

Answer 2

NOTE:

V = Velocity of sound in air.
Vr = Velocity of the receiver or person.
Fs=Frequency of the source or whistle.
F = Freq. as heard by the person.

Answer 3

To find the speed of the train, we can use the Doppler Effect equation. The Doppler Effect is the change in frequency or pitch of a wave for an observer moving relative to its source.

The equation for the Doppler Effect for sound waves is given by:

Δf/f = v_obj / v_source

Where:
- Δf is the change in frequency or pitch of the sound wave
- f is the original frequency of the sound wave (in this case, 540 Hz)
- v_obj is the velocity of the observer (in this case, the person standing near the railroad crossing)
- v_source is the velocity of the source (in this case, the train)

We want to find the speed of the train, so let's rearrange the equation to solve for v_source:

v_source = (Δf/f) * v_obj

We are given the initial frequency of the whistle (f = 540 Hz) and the final frequency after the train has passed (Δf = 540 Hz - 470 Hz = 70 Hz).

Now, we need to determine the velocity of the observer (v_obj). In this case, the person is standing next to the railroad crossing, so their velocity is 0 m/s relative to the crossing and train.

v_obj = 0 m/s

Now we can calculate the speed of the train (v_source):

v_source = (70 Hz / 540 Hz) * 0 m/s
v_source = 0 m/s

It appears that we have obtained a result of 0 m/s for the speed of the train. This suggests that there might be an error in the given problem or measurements, as it is highly unlikely for a train to have a speed of 0 m/s. It's possible that there may be additional information or factors that need to be considered to accurately determine the speed of the train.