An object producing a sound with frequency 500 Hz is traveling at 40 m/s toward an observer, and the observer is traveling at 30 m/s away from the source. Another source producing a sound with the same frequency is traveling at 10 m/s toward a stationary observer. Determine the frequencies perceived by each of the observers, assuming that the speed of sound in air is 345 m/s. Are the two frequencies the same? If not, what causes the difference between the perceived frequencies?
f' = f*(v+vo)/(v-vs)
v = speed of sound = 345 m/s
vo = speed of observer toward source
vs = speed of source toward observer
The Attempt at a Solution
I've figured out that the frequency perceived by the first observer (traveling at 30 m/s) is 516 Hz, while the frequency perceived by the second observer (stationary) is 514.9 Hz.
I understand mathematically why this happens. What I can't figure out is what physically occurs that would make the frequencies perceived by the two observers differ when the relative velocities between the observer and the source are the same in both cases.
Thanks in advance for any help you can give me.