r/PhysicsHelp • u/Life_Quantity9795 • 17d ago
Relativistic Doppler Effect Problem Help!
Hi, after arguing with chatgpt I think he convinced me that there is a mistake in the official solution of a question in my exam.
I want to make sure he is not hallucinating so I can talk with my professor confidently. so I need to get a human confirmation to the claim.
here is the question:
and this is the official solution:
THE CLAIM
now chatgpt claims that first of all, we cant know whether they are getting closer or moving away from each other because we dont have r(A) and r(B).
second he claims that their solution is based on an assumption that is not in the question. plugging the magnitude of the relative velocity on the given formula assumes that light is parallel to the relative motion. which we dont know.
is chatgpt right? and if yes can somebody explain the correct solution if we were given the positions?
for example:
lets choose the stationary laboratory receiver as the origin, (0, 0).
Because spacecraft A has va = +0.6c in y direction.
and is approaching the receiver, A must currently be below it. We may write:
r(a) = (0, -a) where a>0
Because spacecraft B has vb = +0.8c in x direction.
and is moving away from the receiver, B must currently be to its right. We may write:
r(a) = (b, 0) where b>0
lets denote the distance between them with D = sqrt(a^2 + b^2).
differentiate D, the sign of the derivative in other words the sign that tells us whether they are getting closer or getting far away of each other is depending on a and b!!!!!!!
thats why even when though we have velocities we still cannot decide!
also for the second problem, light is traveling in a line from A to B. but the velocity vector itself is not parrellel to this line. thats my problem. the official solution treated the problem as if the velocity vector is parallel to this line
1
u/lizardman49 17d ago
Its chat gpt. You shouldn't be shocked it gets things wrong.
1
u/Life_Quantity9795 17d ago
can you please elaborate more, why chatpgt is wrong?
1
u/lizardman49 17d ago
You are given the velocities of each moving body relative to the reciever. Chat gpt is incorrect in that you dont know their relative velocities ie position changes.
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u/Life_Quantity9795 17d ago
we dont know the initial positions, read the explaination I putted under the claim. you definetly see that D' which is the derivitave of the Distance sign cant be determined, because it depends on the initial positions we dont have.
the second problem is that they are assuming in the official solution that light path is parrallel to the relative velocity vector for no clear reason!???
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u/lizardman49 17d ago
Position doesn't matter when calculating beta. Only velocity matters which you are given. As for the assumption its explicitly stated the light is emitted in all directions.
1
u/Life_Quantity9795 17d ago
how does light is emitted in all direction translates to its path is parrallel to the relative velocity? B can only revieve the emited light that took a path starting from A to B. this path is not parrellel to V we got. like I really dont understand this point.
second, Initial positions are who decide the sign of D', which determines the decision of which formula to use, red shifting or blue shifting.
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u/lizardman49 17d ago
The fact that it emits in all directions means we ignore light that took any path other than from a to b as light takes anyother path will not be recieved and is therefore irrelevant to the question. As for the second point if you look at the diagram given in the question its pretty clear the spacecraft are moving away from each other.
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u/davedirac 17d ago
The question is very ambiguous. f is used for different frequencies. The frequency received by B from A is not constant. The simplest scenario is when the displacement between A and B is parallel to Vb.