A train whistle is heard at 280Hz as the train approaches town. The train cuts its speed in half as it nears the station, and the sound of the whistle is then 270 Hz.
What is the speed of the train before slowing down?
What is the speed of the train after slowing down?
To find the speed of the train before and after slowing down, we can use the Doppler effect formula:
f' = f * (v + vr) / (v - vs)
where:
f' = observed frequency
f = source frequency
v = speed of sound
vr = speed of the receiver (observed object)
vs = speed of the source (emitting object)
First, let's calculate the speed of the train before slowing down:
Given:
f' = 270 Hz
f = 280 Hz
We also know that the speed of sound, v, is constant. Let's assume that v = 343 m/s (the speed of sound in air).
Rearranging the Doppler effect formula, we have:
(v + vr) / (v - vs) = f' / f
Substituting the known values, we get:
(343 + vr) / (343 - vs) = 270 / 280
Now we can solve for vr:
Cross multiplying, we have:
280 * (343 + vr) = 270 * (343 - vs)
Simplifying the equation:
95920 + 280vr = 92810 - 270vs
Rearranging:
280vr + 270vs = 92810 - 95920
280vr + 270vs = -310
We have one equation and two unknowns. We need more information to solve for vr and vs.
So, we cannot determine the speed of the train before slowing down with the given information.