I had a question about how to apply the Doppler Effect equation, which is:
f(0) = f(s) (v+v(0))/(v+v(s))
where
f(0) is the frequency perceived by the observer
f(s) is the frequency as actually emitted
v is the speed of the wave in the given medium
v(0) is the velocity at which the observer moves, which is positive if the observer moves toward the source and negative if the observer moves away
v(s) is the velocity at which eh source moves, negative if toward, and positive if away from the observer.
Now my question is, why is the answer slightly different relative to whom is moving, the observer or the sound. So lets say the observer is moving towards the sound at 10m/s, you would get:
(v+10)/v
But if instead the sound is moving towards the observer, you get
v/(v-10)
These two answers are slightly different. Shouldn't they be the same, since in this frame, nothing is accelerating, and so velocity should be relative and you should be able to switch it up who is moving and by how much. Or is that assumption incorrect?
f(0) = f(s) (v+v(0))/(v+v(s))
where
f(0) is the frequency perceived by the observer
f(s) is the frequency as actually emitted
v is the speed of the wave in the given medium
v(0) is the velocity at which the observer moves, which is positive if the observer moves toward the source and negative if the observer moves away
v(s) is the velocity at which eh source moves, negative if toward, and positive if away from the observer.
Now my question is, why is the answer slightly different relative to whom is moving, the observer or the sound. So lets say the observer is moving towards the sound at 10m/s, you would get:
(v+10)/v
But if instead the sound is moving towards the observer, you get
v/(v-10)
These two answers are slightly different. Shouldn't they be the same, since in this frame, nothing is accelerating, and so velocity should be relative and you should be able to switch it up who is moving and by how much. Or is that assumption incorrect?
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Your assumption is incorrect because the situations are not symmetric with respect to the medium.
Lets take the example to the extreme and assume a propagation speed of 10m/s. Then if the observer moves away at 10m/s the sound will never reach the observer. But if the source moves away at 10m/s, sound will still reach the observer. And the equations show this to be true:
observer moving away (-10 + 10) / 10 => 0. No frequency, no sound.
source moving away 10 / (10 + 10) => 1/2 f Frequency is only halved.
Lets take the example to the extreme and assume a propagation speed of 10m/s. Then if the observer moves away at 10m/s the sound will never reach the observer. But if the source moves away at 10m/s, sound will still reach the observer. And the equations show this to be true:
observer moving away (-10 + 10) / 10 => 0. No frequency, no sound.
source moving away 10 / (10 + 10) => 1/2 f Frequency is only halved.
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I had the same confusion when I first encountered the Doppler equation. Basically, the reason has to do with the fact that the sound waves travel from the source to the observer through some medium (usually air), so you can't just account for the observer's motion directly relative to the source. Instead you have to indirectly account for that relative motion, by first accounting for the source's motion relative to the medium and and then the source's motion relative to the medium.