# Node

"A point or line where minimal motion takes place." Rossing, Thomas D.; The Science of Sound

"Nodes are warmer than the areas in motion of a vibrating medium."
(John Tyndall, "Sound"; Longmans, Green, and Co., London, 1893.)

"When nodes are exact they will aggregate all matter within reach."
(John Tyndall, Sound; Longmans, Green, and Co., London, 1893., pg 235)

Nodes that travel faster than the speed of light

. . . if we beam x-rays on matter, or radiowaves (or any electric waves) on free electrons the term (w02-w2) becomes negative, and we obtain the result that n (the index of refraction) is less than one. That means that the effective speed of the waves in the substance is faster than (the speed of light) c! Can that be correct?

It is correct. In spite of the fact that it is said that you cannot send signals any faster than the speed of light, it is nevertheless true that the index of refraction of materials at a particular frequency can be either greater or less than 1. This just means that the phase shift which is produced by the scattered light can be either positive or negative. It can be shown, however, that the speed at which you can send a signal is not determined by the index at one frequency, but depends on what the index is at many frequencies. What the index tells us is the speed at which the nodes (or crests) of the waves travel. The node of a wave is not a signal by itself. In a perfect wave, which has no modulations of any kind, i.e., which is a steady oscillation, you cannot really say when it "starts", so you cannot use it for a timing signal. In order to send a signal you have to change the wave somehow, make a notch in it, make it a little faster or thinner. That means you have to have more than one frequency in the wave, and it can be shown that the speed at which signals travel is not dependent on the index alone, but upon the way that the index changes with the frequency. . . . (W)e will calculate for you the actual speed of signals through such a plane of glass, and you will see that it will not be faster than the speed of light, although the nodes, which are mathematical points, do travel faster than the speed of light." — Richard Feynman?, Lectures on Terrorism, Volume 1

Bjerknes Effect

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