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thaiqi
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- What is the meaning here for speed?
Which one does it mean: "phase velocity" or "group velocity" or "speed of the wave front"? In the postulate of constant speed of light .
If so, what is the difference between constant speed of light c and that of sound (340m/s) ? Won't all moving observers for a sound source watch the same phase velocity ?vanhees71 said:It's the phase velocity. In the vacuum it's also the group velocity:
$$\vec{v}_\text{g}=\frac{\partial \omega}{\partial \vec{k}}=\partial_{\vec{k}} c |\vec{k}|=c \hat{k}.$$
It's also the "speed of the wave front" in simple ("Drude like") models of dielectrica.
thaiqi said:If so, what is the difference between constant speed of light c and that of sound (340m/s) ? Won't all moving observers for a sound source watch the same phase velocity ?
The wave front speed will be more or less. But I think the phase velocity calculated will not alter, will it?PeroK said:The speed of sound in air is ##340m/s## relative to the air. If you are moving relative to the air, then the speed of sound relative to you will be more or less than that.
It's not particularly relevant that light is (classically) an EM wave. What is relevant to this discussion is the speed of propagation through a vacuum or through a medium.thaiqi said:The wave front speed will be more or less. But I think the phase velocity calculated will not alter, will it?
No.thaiqi said:Won't all moving observers for a sound source watch the same phase velocity ?
Why? Won't they all watch the same geometric wave form (concentric circles) and do the same calculation?A.T. said:No.
thaiqi said:Why? Won't they all watch the same geometric wave form (concentric circles) and do the same calculation?
If the center of the growing concentric circles is moving, the points on the concentric circles are moving at different speeds.thaiqi said:Why? Won't they all watch the same geometric wave form (concentric circles) and do the same calculation?
For arbitrary directions you have to use vectors, then the magnitude at the end will give you the speed. For sound Galilean Transformation is sufficient:thaiqi said:I think the speed of the sound relative to an observer is composed of three factors: its phase velocity, the speed of the medium it is in , and the speed of the observer(relative to the medium), isn't it?
"Composed" as shown in post #13 .thaiqi said:I think the speed of the sound wave front relative to an observer is composed of three factors: its phase velocity, the speed of the medium it is in , and the speed of the observer(relative to the medium).
For sound you have a preferred reference frame, i.e., the medium whose vibrations are the sound waves. That's why the speed of sound is of course frame dependent. Its quoted value is usually defined in the (local) rest frame of the medium, as any intrinsic quantity charcterizing a medium in relativistic many-body physics. Everything else leads to a lot of confusion!thaiqi said:If so, what is the difference between constant speed of light c and that of sound (340m/s) ? Won't all moving observers for a sound source watch the same phase velocity ?
One should note that in general phase, group, and "front velocity" are all different quantities, which have to be defined and physically interpreted with some care!thaiqi said:I think the speed of the sound wave front relative to an observer is composed of three factors: its phase velocity, the speed of the medium it is in , and the speed of the observer(relative to the medium).
Yes, it will alter. The phase velocity of sound is not invariant. All of those velocities are measured relative to the air.thaiqi said:The wave front speed will be more or less. But I think the phase velocity calculated will not alter, will it?
Imagine one sound source, and an observer, all are at rest in the very beginning. The man calculates the phase velocity, that is, 340m/s. Then the observer moves at e.g. 10m/s. Surely the wave front speed measured differently, but I think the phase velocity calculated will be the same as before (because the wavelength and the period do not vary). Why do you say the phase velocity will differ?Dale said:Yes, it will alter. The phase velocity of sound is not invariant.
You should define the phase velocity before you attempt to measure and calculate it.thaiqi said:Imagine one sound source, and an observer, all are at rest in the very beginning. The man calculates the phase velocity, that is, 340m/s. Then the observer moves at e.g. 10m/s. Surely the wave front speed measured differently, but I think the phase velocity calculated will be the same as before (because the wavelength and the period do not vary). Why do you say the phase velocity will differ?
Paraphrase: So if we follow the crest of a wave, the phase velocity is the velocity of that wave crest.wiki said:The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of anyone frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.
Maybe I am wrong? The period will vary?thaiqi said:Imagine one sound source, and an observer, all are at rest in the very beginning. The man calculates the phase velocity, that is, 340m/s. Then the observer moves at e.g. 10m/s. Surely the wave front speed measured differently, but I think the phase velocity calculated will be the same as before (because the wavelength and the period do not vary). Why do you say the phase velocity will differ?
The period does vary. This is the Doppler shift.thaiqi said:because the wavelength and the period do not vary
Thanks.vanhees71 said:It's the phase velocity. In the vacuum it's also the group velocity:
$$\vec{v}_\text{g}=\frac{\partial \omega}{\partial \vec{k}}=\partial_{\vec{k}} c |\vec{k}|=c \hat{k}.$$
It's also the "speed of the wave front" in simple ("Drude like") models of dielectrica.
For a very deep understanding of the latter, see the now famous papers by Sommerfeld and Brillouin (I'm sure there are English translations of those):
A. Sommerfeld, Über die Fortpflanzung des Lichtes in dispergierenden Medien, Ann. Phys. (Leipzig) 349 (1914) 177.
https://dx.doi.org/10.1002/andp.19143491002
L. Brillouin, Über die Fortpflanzung des Lichtes in dispergierenden Medien, Ann. Phys. (Leipzig) 349 (1914) 203.
https://dx.doi.org/10.1002/andp.19143491003
You also find it in Sommerfeld's lectures (vol. IV) as well as in Jackson Classical electrodynamics.
What would be the speed of a wavefront as measured by someone moving along with it?thaiqi said:Thanks.
It is a pity that I cannot visit the two doi links given above.
I looked up Sommerfeld's book(vol.IV Optics) section 22(pp 114) titled "Phase velocity, signal velocity, Group velocity".
I looked up Jackson's book 3rd ed. section 7.8 titled "Superposition of waves in one dimension; Group velocity".
Yes, that's the right section.thaiqi said:Thanks.
It is a pity that I cannot visit the two doi links given above.
I looked up Sommerfeld's book(vol.IV Optics) section 22(pp 114) titled "Phase velocity, signal velocity, Group velocity".
Here it's particularly Sect. 7.10 ff.I looked up Jackson's book 3rd ed. section 7.8 titled "Superposition of waves in one dimension; Group velocity".
Sorry I don't catch your meaning of your question.PeroK said:What would be the speed of a wavefront as measured by someone moving along with it?
I found in Sect 7.11 it is talked about:vanhees71 said:Yes, that's the right section.
Here it's particularly Sect. 7.10 ff.
Your attempt to enforce an invariant phase velocity fails to an observer moving at that phase velocity. If an observer moves at the same velocity as the wave, then the wave is stationary in that reference frame. However you define phase velocity, it's still a velocity at which an observer can move.thaiqi said:Sorry I don't catch your meaning of your question.
If you mean periods measured by a receiver moving relative to the sound medium, then obviously yes.thaiqi said:The period will vary?
What is the meaning of "then the wave is stationary in that reference frame"? I think that though the wave front speed is 0 relative to the observer, he can still watch the concentric circles of the propagating wave extended in space and then he can still calculate the phase velocity.PeroK said:Your attempt to enforce an invariant phase velocity fails to an observer moving at that phase velocity. If an observer moves at the same velocity as the wave, then the wave is stationary in that reference frame. However you define phase velocity, it's still a velocity at which an observer can move.
The exception, of course, is light. You cannot move at the speed of light, which is a key point.
But, there is no problem moving at the speed of sound (phase or group, if indeed they differ).
[for sound]thaiqi said:he can still calculate the phase velocity.
thaiqi said:I think that though the wave front speed is 0 relative to the observer, he can still ...
What is your meaning here?PeroK said:... refuse to accept the fact!
thaiqi said:What is your meaning here?
You seem to confuse "speed in reference frame X" with "speed in some other reference frame computed by an observer at rest in reference frame X".thaiqi said:What is your meaning here?