A train moving at a constant speed is passing a stationary observer on a platform. a flute player is playing a note with frequency of 940Hz. after the flute has passed, the observer hears the sound frequency of 915Hz. What is the speed of the train? The speed of sound in air is 343m/s.

http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/dopp.html

To find the speed of the train, we can use the formula for the Doppler effect:

f = ((v + vr) / (v + vs)) * fo

Where:
- f is the observed frequency
- vr is the velocity of the receiver (observer)
- vs is the velocity of the source (flute player)
- fo is the original frequency of the sound
- v is the speed of sound in air

In this scenario, the observer is stationary, so vr is 0. The original frequency (fo) is given as 940Hz, and the observer hears a frequency (f) of 915Hz. We want to find the velocity of the source (vs), which is the velocity of the train.

Let's plug the known values into the formula and solve for vs:

915 = ((v + 0) / (v + vs)) * 940

Now, let's simplify the equation and solve for vs:

915(v + vs) = 940v
915v + 915vs = 940v
915vs = 940v - 915v
915vs = 25v
vs = (25v / 915)

Finally, substitute the speed of sound (v = 343m/s) into the equation to find vs:

vs = (25 * 343) / 915
vs ≈ 9.39 m/s

Therefore, the speed of the train is approximately 9.39 m/s.