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Dale
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Here is a good source on Doppler, which presents the acoustic and light in a reasonably well unified framework.
http://www.mathpages.com/rr/s2-04/2-04.htm
http://www.mathpages.com/rr/s2-04/2-04.htm
Nugatory said:Things don't "belong" to a reference frame. A reference frame is just a convention for using numbers to describe the position of an object at any given moment. We have this air molecule, and you might say that it's two meters east of you while I say it's five meters west of me - it's the exact same air molecule in the exact same place and we're using different reference frames to describe its position. There's no reason why it's more "my" air molecule at position -5 than it is "your" air molecule at position +2.
GerryB said:In any science text I have read on the classical Doppler effect, there is one set of formulas for the source approachig the receiver, or moving away from the receiver. There is another set of formulas for the receiver approaching the source, or moving away from the source. And they are noticably different.
DaleSpam said:The velocity in the classical Doppler is the velocity wrt the medium. You can distinguish between source moving wrt the medium and receiver moving wrt the medium according to the classical formula. However, you cannot distinguish between a moving and a stationary medium even classically.
DaleSpam said:Here is a good source on Doppler, which presents the acoustic and light in a reasonably well unified framework.
http://www.mathpages.com/rr/s2-04/2-04.htm
PeterDonis said:The formulas for approaching vs. moving away should certainly be noticeably different, yes. For approaching, the observed frequency at the receiver should be higher than the emitted frequency at the source; but for moving away, the observed frequency should be lower. The formula you wrote down for the moving source case (the one with vs) says the opposite.
But the formulas for source moving vs. receiver moving should be the same once you specify approaching or moving away. That's a simple consequence of the principle of relativity, and classical physics obeys the principle of relativity. Classical physics uses Galilean transformations instead of Lorentz transformations to mathematically realize the principle of relativity, but for speeds much less than the speed of light the two are the same.
I suspect that you have misread whatever reference you used. Can you give a specific reference that you are interpreting the way you describe?
DaleSpam said:Here is a good source on Doppler, which presents the acoustic and light in a reasonably well unified framework.
http://www.mathpages.com/rr/s2-04/2-04.htm
Yes, they do account for the scenario, and they do not support the idea that the speed of sound is frame invariant. Do you understand that now?GerryB said:The classical Doppler formulas do account for the scenario you have described.
No it doesn't. It never once shows that. It is very consistent in using ##c_s## for the speed of a signal and c for the invariant speed.GerryB said:This is an excellent link. It shows the usage of c as the symbol for sound.
GerryB said:Well Peterdonis, I first read this in Tipler Physics, but I have seen it in many other places as well, as I mentioned above:
http://en.wikipedia.org/wiki/Doppler_effect
GerryB said:The galilean transformation offers up two different values for one and the same particle (velocity, position, etc.) Which value is the truth, which is the REAL value?
DaleSpam said:The symbol j is used for the imaginary number and current density. The symbol ##\Omega## is used both for electrical resistance and the spatial part of a metric. The symbol f is used for both frequency and function. The symbol x is used for space and for an arbitrary unknown quantity. The symbol ##\phi## is used for potentials and for phase angles. And so forth.
Sound and light are both waves, so they share many substantive similarities (propagation, reflection, refraction, diffraction, energy, phase, frequency, amplitude, etc.). The use of the same symbol is not substantive, it is mere trivia or semantics.
Can you phrase your question in terms of physics, or are you actually interested in such trivia/semantics as the symbols used.
Sometimes there is, but often there is not. For instance color charge or the names of the quark and its flavors. Regardless of the reasons for the choice of a symbol, it is semantics, not physics. Experimental results don't care what symbols we use nor why we use them. "A rose by any other name..."GerryB said:But in physics I would expect that there are some very specific reasons that physicists have chosen certain terminologies to communicate with other physicists.
GerryB said:But in physics I would expect that there are some very specific reasons that physicists have chosen certain terminologies to communicate with other physicists.
DaleSpam said:"A rose by any other name..."
Nugatory said:When you're writing down your ideas for others to read, it's advantageous to use whatever convention will be most familiar to the largest number of your potential readers, so once a convention is established it tends to become dominant.
So we agree. Then please ask your question in terms of the meanings rather than the symbols. So far, it seems as though you are asking about the ink on paper rather than the physics.GerryB said:The ink on paper, the symbols, may not be important, but the meanings behind those symbols is of life and death importance.
DaleSpam said:So we agree. Then please ask your question in terms of the meanings rather than the symbols. So far, it seems as though you are asking about the ink on paper rather than the physics.
DaleSpam said:To my knowledge "invariance" has only one meaning in special relativity. It means that a quantity or an equation does not change under the Lorentz transform. Is that not your understanding also?
GerryB said:Will these two observers use the same formula: L = ct + vt? This formula describes the idea that as the sound wave (velocity, c) travels rearward, it meets the caboose (velocity, v) traveling forward during the sane time. Each begins at the endpoints of the distance, L. This formula can be rearranged to the MM form: L / (c + v) = t; v = [L / t] - c, to find the velocity of the train relative to the earth.
Even in Galilean relativity it is clear that the speed of sound is frame variant. In fact, in Galilean relativity ALL finite speeds are frame variant.GerryB said:Well I agree with your definition of invariance in STR, but I think invariance has meanings beyond that. Since gallean transformations are contained within STR, but are negligible at the speeds of an average train, we can still use the old formulas. In classical galilean transformations, acceleration, distance intervals, and time intervals are also invariant quantities. So I am speculating that the observers in two reference frames moving relative to one another will measure the same velocity c for the sound wave, then I speculate that the equation I presented in my first post is valid. But it is only speculation, which is why I have asked the question.