# Standing Electromagnetic Waves

A standing wave can be produced in a guitar string where the wavelength of the wave is the same length as the string (I believe this is referred to as the first harmonic) and where the string is an exact multiple of the wavelength of the wave (referred to as the second and subsequent harmonics).
A standing wave of light can apparently be produced by propagating the wave between two mirrors placed an exact multiple of the light's electromagnetic wavelength apart. I first thought this principle might be used in a laser but later realised the waves didn't need to exactly superimpose to increase the intensity of the resulting laser beam of light.
My thoughts then turned to electromagnetic waves more generally - under what circumstances (if any) would an electromagnetic wave be able to achieve a standing (presumably spherical) form bound by the strength of its own electric and magnetic fields (while sound propagation requires a medium such as a guitar string, electromagnetic waves can propagate in a vacuum)? Can the strength of the electric and magnetic fields ever be great enough to bound particular electromagnetic (presumably shorter) wavelengths ?
Some secondary questions are:
Would such a standing wave also support multiple harmonics ?
Noting that the "v" in v=fγ refers to speed rather than velocity, would the speed of such a standing electromagnetic wave still be "c" even though it may propagate circularly?
I Assume the formula breaks down somewhere in that if you propagate a wave with infinite energy and the frequency becomes infinite, presumably the wavelength would become zero and the speed also would then become zero (ie you pour enough energy in and the wave just disappears like a black hole).
While electromagnetic waves are considered to have duality the energies of the wave and particle form are supposedly linked by the same formula - assuming that there could exist standing wave forms of electromagnetic waves, perhaps that is what a photon is ?

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f95toli
Gold Member
"standing" electromagnetic waves are very common, a lot of microwave technology (mobile phones etc) is based around setting up standing waves in various structures. A simple example would be a cavity with a length lambda/2 which works as a bandpass filter; lambda/4 /8 etc are also useful as stubs etc.

sophiecentaur
Gold Member
2020 Award
@wallabyted
I don't think that a standing em wave could exist, in the absence of any imposed boundaries. The reason for a standing wave being sustained is the when there are reflections at some change in the medium. Also, space is a linear medium, em fields do not interact - they just add up - so I don't think your idea of a self-sustained standing wave structure is possible. I think you may have some Star Trek weapon scenario in mind?

Yes, there are many examples of standing waves with more than one overtone* present. A vibrating guitar string is a typical example; it doesn't just produce a 'pure' sunusoidal tone.

*I use the term 'overtone' rather than harmonic because the modes of oscillation in many structures are very often not exactly harmonically related when the geometry is frequency dependednt. This may be because the speed of all waves may not be the same or because the actual positions of the 'ends' or boundaries may be different for different frequencies. Listen to the ghastly noise that beginners on the trumpet can make when they don't know about 'pulling' the pitch of some of the higher overtones to get the right frequency.

Electromagnetic standing waves do exist. If you have some extra cheese or chocolate at home, you can even test it, you will also need a microwave oven. First you'll have to mess around with the microwave itself. You have to make the food-rotating-tray NOT turn around as it usually does. How you do that depends on your oven, but it's usually not a difficult task.

Next step is to take a large plate and put the chocolate or cheese on it, so that they cover the whole plate. Put the plate in the microwave and warm it for a few seconds (depends on the performance of your oven), but not too long, otherwise the whole thing will melt apart. If you do it right, when you take it out, there should be parts that are melted better than the others. These more melted parts are the signs of where the microwave had anti-nodes, or "maximum displacement" causing more heat. These areas should be equidistant, so if you were to measure their distance, look at the wave frequency the microwave emitted (usually written on the back of it or something), then based on your measurements you could "measure" the speed of light. :)

The rotation is built into microwaves for the very reason that standing waves occur, and some parts of the food will remain completely cold while others will be extremely hot.

True it's not a sight, and it's a 3 dimensional standing wave, hard to imagine. 1 dimensional ones are those created in the old fashioned antenna's... the antenna being the resonator itself. It's an em standing wave, even though it doesn't involve light.

em fields don't interact, but then no standing wave requires interaction. Superposition, or in other words addition is sufficient.
Peace! :)

Neat trick. If you stacked several layers, would you get a 3D pattern? Or--would the layers block too much of the radiation?

Second thought. Doesn't the shielding (cabinet) of the microwave oven serve as a resonating space (grounded metal walls all around) and therefore supply the required enclosure/structure as mentioned above that causes the standing pattern?

Wow and I haven't even drank any coffee this morning.

DC

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:) Probably stacking them up would block too much radiation, thinking of some of the big pots warmed up in the microwave staying cold in the core... :) But a lot depends on what you use. Also, if you did find something that would work, you would get a completely different picture compared to what happens when the microwave only has some food at the bottom. That's because EM waves travel at different speeds in different mediums, so when you fill the microwave with cheese, the pattern will be completely different compared to the pattern that would be in air.

Mapping that 3d pattern is something I've thought about too... :) I've thought of trying to raise the tray with cheese to different levels using maybe sticks or something... But then the tray in the middle of the air will also distort the picture, so I don't know... :)

The shielding is not the resonator, the shielding is only to shield us from the waves, and to provide a kind of a "mirror" for the waves to bounce back at each other, interfering with each other causing the pattern. So technically the wave itself is the resonator, or the photons. But the shielding is pretty important though :)

Good morning! ^^ It's evening here...

sophiecentaur
Gold Member
2020 Award
The standing wave is only there because of the walls of the oven. What else would make the waves double back on each other and interfere?

Ok, "still pretty important" was an understatement, but still, it's not the resonator, because the resonator is what actually resonates. The walls don't resonate, but they are needed for the EM waves to interfere and therefore resonate... :)

sophiecentaur
Gold Member
2020 Award
That's just semantics.
The box is called a Resonator.

Yep.

As for the other part. Interesting. How about a stack of dielectric plates with small separators (also dielectric) in between? Each plate coated with some normally grainy, water-bearing paste. A very thin coating on one side only. Pick a paste. Flour/water?

Or--some plastic-like film that has dissolved water in it's structure. Very fine synthetic fabric, slightly moistened? Nah, boiling point not hot enough?

Three dimensional electromagnetic standing wave plotting.

Someone has done this already, right?

DC

I like the cheese/chocolate in the Microwave trick.

@sophiecentaur
yep I get that a reflective surface "can" bound a standing wave (and I have no interest in any super weapons :-) ), but I thought that an electromagnetic wave was pretty much the only wave I knew of that didn't require any material medium to propagate in - so I thought there may also be some circumstance where the wave could be reflected upon itself without external interference, and the most likely scenario I thought of was if the wave pulled itself into a circle/sphere given the electric and magnetic fields would always be at right angles to each other and another thought (right or wrong) that an EM wave could "twist" around its own longitudinal axis.

delej mentioned that EM fields don't interact - though I thought the magnetic field strength is usually proportional to the electric field strength, which I assumed would be an interaction in itself. I think my old high school physics teacher once even suggested that the magnetic and electric fields propogate each other.

Perhaps the spherical interaction I was picturing could only occur at higher power densitys and field strengths. Do higher EM power densitys only occur at the higher energy/frequency end of the EM spectrum ? Maybe even multiple EM waves could intersect at (exact) different angles and interact in such a way as to "orbit" around one another in a standing pattern (this almost hurts my head to think about).

Don't some radio transmissions experience radio frequency interference with other frequencies ? Or is this always just splattering (ie some of the signal being transmitted at the same frequency as the signal interfered with - or perhaps an inability of the tuning circuitry to deal with the extra signal).

Something that probably sparked this line of thought was something I read that suggested macro to micro astronomical objects move simarly to each other and to objects at the atomic level so I thought this may be a recurring pattern from the largest to the smallest scales of things - including EM waves.

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sophiecentaur
Gold Member
2020 Award
A linear medium is a linear medium. Space appears to be linear so why should fields of any amplitude interact in space. Of course, in non-linear media, the sum of two em waves of high enough amplitude can produce other artifacts (intermodulation and cross modulation products) but that's a different matter. Radio signals can intermodulate in transmitters, receivers and in the ionosphere - they are all non-linear. Two intense laser beams can also be made to intermodulate - but only in a suitable material.
You can't isolate electric fields from magnetic fields, ever. Your teacher told you the correct thing. When there's one, there has to be the other. There is no truly static field (electric or magnetic) because any field has an existence between being turned on and turned off - the change, producing the other field (at possibly a very low level but still there). Once launched into space, Electric and Magnetic fields vary at the same frequency, in phase, at right angles to the direction of propagation and to each other and their relative 'strengths' are always the same (in free space).

Afaik, given a powerful enough gravitational field (god knows how and what shape you'd need) you could, I suppose arrange to channel a beam of light into a looped path but that wouldn't just involve electric or magnetic fields. I don't think that space and em, on their own, could do that, though.

Referring to one paragraph I will add that the radio frequency "mixing" doesn't take place in space prior to receipt, but rather in the radio circuits where it is no longer an EM radiation but rather a conducted current.

SC, your writing is very clear and precise; you must have been an excellent teacher (which I have found to be rather rare.)

DC

sophiecentaur
Gold Member
2020 Award
Referring to one paragraph I will add that the radio frequency "mixing" doesn't take place in space prior to receipt, but rather in the radio circuits where it is no longer an EM radiation but rather a conducted current.

SC, your writing is very clear and precise; you must have been an excellent teacher (which I have found to be rather rare.)

DC

Cheers for the comment.
Have you not heard of Ionospheric Non-inearity or Ionospheric mixing? It is a not-uncommon mechanism by which high power transmissions can drive regions of the ionosphere into non-linearity. A weaker signal can have the interfering modulation impressed on it even when the receiver only gets the interfering signal itself at a low level.
Of course, it's not free space but a 'medium, that's involved.

Ok, I've realized that you were right, the box itself is called the resonator, and a knew that previously, I just mixed things up the last time... On the other hand when I was only quoting sophiecentaur about EM fields not interacting. I think we were both talking about EM waves in this case, photons by the particle model... Otherwise it is true what you're saying... But if I'm wrong I'll leave it up to sophiecentaur... I don't teach (nor have taught) physics :)

SC. Yes on the ionosphere stuff. Imagine I heard the results of that quite a bit when I was a young amateur radio operator (14.) I was just ignoring that part and rather covering the more typical/common phenomenon. Edit: You notice I used the term "space." Backside covered. LOL

Actually just now I was thinking the ionosphere could serve as a down converter, although I had never considered that before. Mostly when I was doing that stuff I was thinking about reflection, or refraction. Skip was the term normally used.

About 15 miles from my home is Central California is a long straight ground structure that turned out to be the remains of a receiving site for an over the horizon radar system. The first time I flew over it I thought it might be a linear accelerator. (I worked at SLAC for a while.) Transmitter site was way down the coast. Must have been very powerful.

You have answered the initial question, so I guess it is OK when we steal the thread? Chuckle.

DC

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