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Technical Accuracy of Article - My Concerns
It is stated in this article that:
The universal wave equation is:
With all the units beautifully clarified, however this is a dispersion relation; not a wave equation:
where is the phase velocity.
The wave equation depends on the physics of the system being modelled.
Also, we must not forget that in a more dense material, EM waves travel slower than in a complete vaccum. I think this article needs major re-working, possibly starting with how a wave propagates. I'm going to work on something to expand this stub also (derivations of wave propogations). Possible candidates being - sound waves in a medium, waves on a guitar string and co-axial cable waves.
Group velocity can be faster than c
I deleted the following paragraph from the article, because it is in general not correct:
"Since classical information and quanta of energy is sent via wave packets (which must consist of a broad range of frequencies), the group velocity cannot ever be greater than the speed of light in a vacuum. This restriction does not apply to the phase velocity and so it can travel faster than the speed of light without violating the laws of special relativity."
In some circumstances, the group velocity can exceed the speed of light in vacuum, e.g. in a higly absorptive medium. This is possible because in general, the speed of the information is NOT equal to the group velocity. See, e.g. Dispersion_(optics). Sorry, I don't have time to rewrite it more accurately.
How wave can propagate
1. A diaphragm of a speaker produces a positive displacement, which pushes a front of air forward, creating a wave that propagates away from the source.
2. The diaphragm of the speaker produces a negative displament in which the diaphragm retracts, which creates a suction/negative pressure. The wave that has moved forth is less likely to be pulled back by the suction because the resultant effect of pushing of air is always stronger than of pulling of air.
3. The negative displacement of air is quickly quenched by air coming by the side, which quickly restore the negatively displaced space to match the ambient pressure.
4. In cases of using larger diaphragm, the quenching of air towards negative pressure is slow because the air needs to travel longer distances from the sides to the centre of the diaphragm, in order to cover the whole diaphragm. Thus, large diaphragm is not able to produce high frequency sounds because the quenching of air is too slow. As a result of applying high frequency mode, wavefront produced by the diaphragm is limited to move forth and be retracted back towards the diaphragm due to the sudden suction effect caused by rapid negative pressure when the diaphragm vibrates in high frequencies. Thus, This is the reason why large diaphragm speakers are not efficient to produce high frequency soundwaves.