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A pressure wave in air travels at the speed of sound. However a voltage wave in a copper conductor travels at a significant fraction of light speed. Why the difference of many orders of magnitude?

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  • $\begingroup$ Are you asking about an “isolated” conductor, or about signal propagation in a transmission line? $\endgroup$
    – rob
    Dec 24, 2022 at 14:10
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    $\begingroup$ A light wave in air travels close to the speed of light. Why is it so much faster than the speed of sound in air? Well, light and sound waves are two very different things obeying different physics requirements. $\endgroup$
    – Jon Custer
    Dec 24, 2022 at 14:39
  • $\begingroup$ An isolated conductor is attached to the positive terminal of a battery. How is the battery voltage "communicated" to the entirety of the wire at light speed. $\endgroup$
    – adlibber
    Dec 24, 2022 at 15:10
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    $\begingroup$ What your question doesn't include is that EM waves travel outside of the wire aswell as inside, as demonstrated in the popular veritasium video, if your question is "An isolated conductor is attached to the positive terminal of a battery. How is the battery voltage "communicated" to the entirety of the wire at light speed." Then you aren't just looking at the speed of an EM wave in copper, you are modelling the EM.waves travelling across the air aswell youtu.be/oI_X2cMHNe0 and youtu.be/bHIhgxav9LY $\endgroup$ Dec 24, 2022 at 16:45
  • $\begingroup$ Did high-school science not show you first that pressure waves travel at the speed of sound? Don't you remember science lessons teaching that in perfect conductors, electricity travels at light speed? Why are you trying to compare the speeds of light and sound? $\endgroup$ Dec 27, 2022 at 0:55

2 Answers 2

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This answer will probably seem lame to you -- for the real answer, take a course in electrodynamics. In the one I took, in my third year in an electrical engineering program, this question was answered about three or four weeks into the course, at least in the context of a parallel-conductor transmission line.

The instructor wrote Maxwell's equations in the upper left corner of the board, and 50 minutes later we had an answer in the bottom left corner of the board.

The short and unsatisfying answer is that at those time scales a conductor does not so much conduct electrons as it guides the electromagnetic field, and that electromagnetic field naturally travels at the speed of light.

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    $\begingroup$ +1. Yet you may want to make it explicit that it is the speed of light in the medium or at the interface (between wire and air / whatever) $\endgroup$ Dec 24, 2022 at 17:04
  • $\begingroup$ Note that the speed has little to do with the nature of the conductor: it's controlled by the stuff around the conductor. So, it doesn't matter that your conductor is copper. $\endgroup$
    – John Doty
    Dec 24, 2022 at 17:22
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    $\begingroup$ It’s sixty years since I did my electrical engineering degree hence my cloudy brain! I would really appreciate a qualitative description on how a battery voltage travels along an isolated conductor connected to its positive terminal. $\endgroup$
    – adlibber
    Dec 24, 2022 at 17:50
  • $\begingroup$ You need to expand your question (and remember your EE classes, to the best of your ability). A truly isolated positive conductor presumes a truly isolated battery, and that's a near-useless case study (short answer: the system acts like a voltage source connected to an antenna with one short side and one long side, and voltage is undefined because the battery-wire system is isolated). $\endgroup$
    – TimWescott
    Dec 24, 2022 at 18:06
  • $\begingroup$ If I connect an AA battery to a 10m length of copper wire I would expect to be able to find the open circuit battery voltage at any point on the wire. What is a qualitative explanation of how the voltage is distributed. Using an analogy with a hydraulic pipe it is self evident how the hydraulic pressure is distributed, but this is electricity! $\endgroup$
    – adlibber
    Dec 24, 2022 at 18:29
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The speed of sound depends on the bulk properties of the medium that is carrying the sound. Generally the speed is:

$$v=\sqrt{\frac{\text{elastic properties}}{\text{inertial properties}}}$$

For a solid, the "elastic property" is the Young's modulus for the substance, and the "inertial property" is its density.

But the transmission of an electric signal doesn't depend on the bulk properties of the conductor, since the signal is carried in the electromagnetic field. The conductor acts as a waveguide, steering the flow of energy carried in the electromagnetic field. The energy is in the em field that surrounds the conductor. The speed of the waves depends only on the electromagnetic properties, but for good conductors separated by good insulators, the speed is always going to be close to the speed of light.

The speed of sound in a solid will be much slower, since it depends on the Young's modulus and density of the matter that make up the conductor. The speed of electricity doesn't. So while the speed of sound will be on the order of several thousand km/h, the speed of electricity will be close to the speed of light, c.

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