We are just finishing sound, and one of my better students found a problem
in the textbook that he was trying to do 2 ways:
1. He took the problem 'as-is', letting both observer and emitter move and
obtained the answer.
2. He took the observer as stationary, and increased the speed of the
emitter by the combined speed of the two and got a different answer.
If I'm not losing my mind, he should've gotten the same answer both ways.
I checked his work and it all seems correct, but I've got to be doing
something wrong, so a second (third, fourth) set of eyes would be welcome...
The problem reads:
Two trains are approaching each other when the train on the left toots its
whistle. The sound has a frequency of f = 525 Hz and the speed of sound is
345 m/s.
*Train* *Speed* *Direction*
One v1 = 150 m/s to the right
Two v2 = 180 m/s to the left
(a) If there is no wind (still air), what is the frequency heard by
the other train?
He and I did:
f_obs = 525 * (345 +180)/(345-150) = 1413 for both moving
and
f_obs = 525 * (345)/(345 - 330) = 12075 if the observer is stationary and
the emitter is closing with the combined speed.
Is it because the combined speed is so close to the speed of sound in the
problem?