# Are waves inside conductor wires considered longitudinal waves, just like sound waves?

Are signals transmitted through electrical wires considered longitudinal waves (signals) or electromagnetic waves?

I think it would make sense for them to be longitudinal because the electrons are pushed then dragged back by the force of voltage or potential difference.

• Your title and your question seem to not fully agree. In the title you ask about logitudinal waves, in the question you ask if they are logitudinal waves or electromagnetic waves. If your logitudinal wave isn't electromagnetic, what is it? Commented Sep 8, 2017 at 8:24
• I though the were transverse waves. Commented Sep 8, 2017 at 8:28
• A wire is a 1-dimensional structure so it doesn't make sense to distinguish between longitdudinal and transversal waves. The essential difference of both is that longitudinal waves are waves of a scalar quantity and transversal waves are waves of a vector quantity. This becomes relevant only if waves propagate in space with more than 2 dimensions.
– Curd
Commented Sep 8, 2017 at 9:50
• This question might be better suited to the physics forum.. Commented Sep 8, 2017 at 11:35
• I think the "longitudinal" waves you imagine are patterns of different electron density. These do exist but they aren't EM waves and they aren't a main property of conductors but insulators and semiconductors. Look up gunn diode for an electronic component which uses "the sound of electrons" to generate microwaves. Commented Sep 9, 2017 at 4:31

Interesting question.

This is one of those questions that gives most EEs a bit of headache because it is rather difficult to get one's brain wrapped around what is theoretically going on with electromagnetic waves. The truth of the matter is it is not quite as simple as we first imagine.

Here is how I rationalise it.

First and foremost you need to separate the notion that electrons have anything directly to do with electromagnetic waves. They don't. EM waves propagate without the need for any material. In a vacuum they propagate at the speed of light, when the wave encounters a material they are slowed by the materials physical properties.

Having grasped that bit of wisdom, it is easy enough to understand that when you apply a voltage to one end of a bit of wire, it takes time for you to be able to detect that voltage at the other end of the wire. That voltage propagates down the wire at the speed of light for that conductor material. In effect you created, or more accurately, changed the E-Field at one end and the change wave takes time to get to the other end.

Now consider instead modulating the applied voltage, that is, applying a signal to the wire. If we break up that signal in the time domain into infinitely small periods you can see from what we just discussed that there will be that propagation delay for the instantaneous change at one end to reach the other. The E-Field must "carry" those changes to the other end. Again, it is important to remember, this has nothing to do with electrons.

So, to summarize so far, the electromagnetic waves are the carrier for your signal not the signal itself. EM waves happen to be transverse, and that does not change.

The signal, or whatever voltage wave you are transmitting, is effectively a modulation of that carrier, and is usually longitudinal. You are setting up, or transmitting, a difference in the electrical field. It's those local differences that excites the electrons in your conductor and make them move in reaction.

Conductors have very high absorption, so EM-waves propagating inside a conductor do not reach very far. An ideal conductor has infinite absorption and EM-waves cannot propagate inside an ideal conductor.

EM-waves propagate in waveguides, which may consist of conductors (e.g. coax cable or twisted pair), however not all waveguides need conductors (e.g. fiber optic cable). Also the energy the wave carries is contained in the field which is mainly in between the conductors. The conductors are only needed for confinement of the wave, i.e. that the wave is going where it is supposed to go and not arbitrarily dispersing into free space.

Whether the waves are longitudinal or not (or have some longitudinal component) depends on the waveguide geometry and the type of mode the EM-wave corresponds to. In most cases waves are a mixture and have both longitudinal and transversal components. Note that in free-space no longitudinal EM-waves can exist (but in waveguides this is possible).

• I would say that the issue here is that the assumption is made that "wave" is confined to the cable, when in fact it is not. Outside of the conductor we have TEM modes propagating the signal, and inducing currents inside the conductor. Because the currents can easily propagate along the cable, so does the wave. At least that is my first-order understanding of the matter. Commented Sep 8, 2017 at 8:36
• @JorenVaes: I am not sure if I understand your comment. Commented Sep 8, 2017 at 12:44

Electromagnetic waves are Transverse in nature. The E and H field oscillate perpendicular to the direction of propagation of wave. If you consider a transmission line such as a coaxial cable, there are two conductors that carry currents in opposite directions. One current flowing from source to load and other from load to source. It is true that these two conductors carry currents. They are separated by a dielectric layer of foam or polyethylene. Your Electromagnetic wave propagates along the gap between the two conductors. The electromagnetic wave is produced due to the jiggling of electrons. As a result of which a self propagating wave is produced for long distance transmission. In a coaxial cable like RG59, RG6 etc the outer conducor is kept to confine the EM wave inside the cable. This is done to tackle skin effect at high frequencies. Moreover, Ron Schmitt's "Electromagnetics Explained" tells that the electrons flowing thro the inner and outer conductors just serve to guide the EM wave inside the dielectric region. For, dielectrics allow EM waves to pass thro them.

The presence of a longitudinal wave requires an extension of Maxwell equations to incorporate this extra piece. In addition, the energy conservation equation should include a term that gives momentum and energy to the longitudinal wave besides the transverse wave. In that case one can say that the longitudinal wave exists at a fundamental level.

When you mention “signals transmitted through electrical wires,” I am assuming you are referring to the voltage/current waves from transmission line theory, NOT the EM waves that others were discussing. These two phenomena are distinct, and the latter is much more complicated to explain and visualize in the setting of charge carriers moving through a circuit. Others are correct in noting that EM waves are transverse in nature (i.e., electric/magnetic field intensity displacement is perpendicular to the direction of wave propagation). However, I don’t think this is addressing your question.

Focusing on the current wave in the wire specifically, I think your intuition is mainly correct. Let me explain:

Consider the classic scenario involving the series combination of a DC voltage source (w/ some series resistance), a power switch, and a lengthy transmission line with some termination scheme. Suppose that the switch has previously been left open for a while so that the T-line is uncharged (no initial conditions). Now, the switch closes.

In your head, imagine dissecting the transmission line into many thin, cross-sectional slices (I’m thinking of a cylindrical coaxial cable as the T-line here). Immediately after the switch closes, electrons (I’ll assume electrons are the charge carriers in this example) in the cross section of wire at the source end are “pushed” (repelled, more accurately) away due to the high local potential. But these electrons that were just shoved down run into more electrons in the adjacent “slice” of cable, so those electrons are now pushed down as well. And so on and so forth.

This series of “pushes” is what constitutes the current wave in this example (transient signals from a DC source), and, logically, the “pushing” (i.e., repelling electric forces) should be in the direction of propagation of the current wave, at least on an average basis. Specifically, the electron displacement local to each “slice” of cable is parallel to the direction of wave travel. So, to answer your question, the current wave in particular is longitudinal indeed, and your analogy to sound waves is accurate (the “pushing” in the case of sound is due to air pressure).

I think there a few useful ways to conceptualize this behavior. For instance, you could view it as a dynamic tradeoff between kinetic and electric potential energy (when the electrons are lumped together vs. when they are pushed away), where the sum of these two is a constant (neglecting thermal dissipation and radiation) that is carried by the wavefront. Electrical engineers in particular usually explain it in terms of a lumped-element model of the “distributed” transmission line: a “pulse-forming” LC network, where the L and C are parasitic inductance and capacitance values, respectively, of the T-line taken on a per-unit length basis. The charging of the parasitic capacitance induces current in the neighboring parasitic inductance, which then dumps charge from the previous capacitance onto the next, etc. This view of “charge-hopping” due to the charging/discharging of an LC ladder provides intuition as to why the voltage/current at the power source of any real circuit does not appear instantaneously at all parts of the circuit: the rate of propagation or “group velocity” is limited by the geometry of the circuit and, if Einstein is right, cannot exceed the speed of light. The “better” the geometry (lower parasitic L/C), the faster current/voltage waves travel.

It is important to note that speed of wave propagation (which is often close to the speed of light) is NOT the same as the electron drift velocity in the circuit (which is often VERY slow, maybe like 1 cm/min - I could be off, but I know it’s slow). This is why I wanted to highlight electron movement local to each slice of cable: just like a stack of dominoes falling, it is not the individual electrons themselves but the “wavefront” (the falling animation of the dominoes) that progress quickly down the cable. Relative to the scale of the wave on the T-line, the individual electrons make micro-adjustment like moves in their respective slices of cable until all the wave reflections die down and normal, steady DC operation ensues (constant current independent of position along the cable).

And to add even more nuance here, we can additionally draw a distinction between the speed of the electrons and their drift velocity. The drift velocity relates to the net change in position (displacement) of charge along the cable in the direction of the current whereas the speed relates to the instantaneous rate of movement of the charge, no matter the direction. In other words, drift velocity is a projection of raw charge speed onto the axis of the cable. The speed is very, very high (maybe an order of magnitude or so below speed of light) due to the constant, random motion induced by thermal energy (this is one source of “noise” in circuits, which is ever present). So, the net effect of stimulating electrons with a potential difference in a closed circuit is really minute at least in terms of the raw speed — it really doesn’t make them go much faster at all!

The drift velocity in particular is very slow due to the absolutely ENORMOUS amount of charge present in each slice of cable (just look up the charge density of some common conductor materials — remember, current is the number of charge carriers that cross a given area per unit time, which is different than current density). So, even if electrons on average make only about 1 cm of progress each minute let’s say, there are SO MANY of them passing any given cross section in the wire, which is really what makes current so significant. In other words, generally, it’s the “bandwidth” afforded by the geometry of conductors that really drives current, not the electron velocity itself (you can think of it as an interstate where cars are only inching along in traffic but with zillions upon zillions (literally) of lanes!!)

P.S. In my transient circuit example, I implicitly drew a connection between current and electron displacement when, in general, conventional current direction is opposite charge carrier displacement. But the results still hold, just in the opposite sense. I usually think in terms of positive charge flow in a circuit, which is why I wanted to clarify here.

• Quick clarification/modification: In general, I don’t believe that “charge pushing” is the most accurate description of current in a circuit: I was mainly referring to the transient (wave propagation/reflection) period in my comment. When the waves “die down” and normal DC mode ensues (voltages/currents are no longer functions of position along cable) as I mentioned, there is a supposed “quasi-steady state surface charge distribution” that is mainly responsible for the current production, as outlined in this paper: matterandinteractions.org/wp-content/uploads/2016/07/… Commented Aug 5, 2023 at 1:12
• It’s an interesting read ^^. But, either way, whether it’s mainly charges internal to the conductor “pushing” each other or this surface charge distribution that is the main contributor to current, the charges have to move from some initial configuration in the first place. And I don’t think this mobilization of charge is only due to electric field lines spawned from the power source because many complications arise in this model when the geometry of the wires/traces is all over the place. I would think that charge pushing is involved to some degree, especially in transient wave periods Commented Aug 5, 2023 at 1:24
• *Complications, specifically referring to electric field boundary conditions between the surface and the air outside the conductor Commented Aug 5, 2023 at 1:32