# Multiple Radio Waves and Superposition

1. Jan 26, 2008

### autek

There are hundreds, if not thousands, of RF signals all around us from those at VLF frequencies to microwave frequencies and I suspect if you set up a very long random length of wire as an antenna, there would be a resulting induced electrical signal that is the sum (and differences) of all those various RF waves hitting it. My question is, does a single composite wave exist in space inducing a similar signal in the antenna or is the signal in the antenna only the composite resultant of a multitude of discrete radio waves hitting the antenna? Does the superposition occur whenever two or more waves meet anywhere in space resulting in a composite wave, or only if there is antenna to receive them?

Similarly, I am familiar with Young’s two slit experiment from looking at various websites and I think I understand destructive and constructive interference, but again, in the absence of the white card to show the bands of interference, is there a single resulting composite wave where the waves meet as the result of superposition or are they two separate waves until you provide the card?

My gut feel is that a composite wave results anywhere two or more waves meet and the antenna and card are just means of detecting what the instantaneous value of that composite wave is for that particular location at that particular point in time, but I would love to know for certain. And more importantly, understand why if that is not the case.

2. Jan 27, 2008

### pam

The radio waves are all incoherent, so there is no interference.

3. Jan 27, 2008

### Staff: Mentor

Unless you have some real need to do so (i.e. considering single-photon events) I would not worry about quantum mechanical effects and I would stick with a purely classical (Maxwell) analysis.

If you look at Maxwell's equations in free space you can easily reduce them to a simple wave equation. The key point to notice in the wave equation is that it is a linear PDE. That means that superposition applies. That in turn means that the solution to a sum of inputs is equal to the sum of the two individual solutions. In other words if you have a transmitter A, a transmitter B, and a receiver C, then the voltage received at C is simply the voltage that would have been received from A alone plus the voltage that would have been received from B alone.

Similarly in free space. If you have the same transmitters A and B, and if you solve Maxwell's equations to determine the electric field at each point in time and space you will find that the electric field due to A and B together is simply equal to the electric field that would have been generated by A alone plus the electric field that would have been generated from B alone. That applies at every point in time and space and you don't even really have to solve the messy PDE to prove it.

Last edited: Jan 27, 2008
4. Jan 27, 2008

### autek

First of all I would like to thank you both for taking the time to reply.

In response to PAM.

I can understand why it has to be coherent to produce the nice banding in Young’s experiment, but I am afraid the rest still eludes me.

Just saying you need coherent signals, doesn’t answer the question in Young’s experiment what happens if the two waves meet in space with no card. Is still there still interference even if the waves are not striking the card? I think if I understood DaleSpam correctly there is.

I also wonder if the frequency of the wave through one slit is varied from the other by one tenth of a hertz why you still wouldn’t have nodes and antinodes even if they don’t produce stationary bands. Is it possible that that rather than stationary dark and light bands, that the bands would appear to move back and forth on the card at a frequency related to the difference in the two frequencies?

I am sorry to be obtuse, but I can understand why you cannot observe the interference if the waves are not coherent, but I don’t understand why they don’t interact at all, even if you cannot directly observe the interaction on the card.

In answer to DaleSpam.

It took me a while to find what PDE means, and I assume it means “partial differential equation”. And you are correct in your assumption. I would prefer not to go there. What education I have is not as a physics or math major. Your explanation is complete and simple enough for me to understand and I appreciate that.

I do however have two follow up questions. If we look at one point in space with respect to time, the variation in the electric field varies in step with the superposition of all the waves at that point over time, whether it is two or two thousand. I think that is what you were saying.

The first question is, isn’t that superposition the result of wave interference just as in Young’s experiment except that it is so much more complex because the individual waves are also complex and not coherent?

Second, looking again at one single point in space, could you not plot the combined electric field value of all the fields (waves) on one axis and time on the other axis, and wouldn’t that plot be a complex wave of that interference, and could we also say that the wave (plot) is representative of a composite wave passing that point over that same period of time?

Or I have stretched your explanation to the breaking point?

5. Jan 27, 2008

### rbj

whether they're coherent or not, it doesn't matter.

superposition does in fact apply. but there are issues.

dipole antennas, by their geometry, will not respond to EM waves that are off of the end of their axis. the EM wave of transmitters that are off of the end of the dipole element do add to the EM wave that is broadside to the element, but the free charge in the element will only slosh back-and-forth (or maybe i should say "left-and-right") from the components of EM waves that are at a right angle to the dipole element.

also, the fact that a dipole element is a fixed and finite length actually makes the antenna element a tuned circuit. the frequency components of the composite EM wave that are at about an integer times c/(2 L) where L is the dipole length, will resonate better than other frequencies. it's a lot like tides of the earth (or sitting in your pretty full bathtub, like Calvin and Hobbes, and sloshing forward and backward - there is a particular rate where the water is happy to slosh with you and get great waves, that is resonance).

6. Jan 28, 2008

### Staff: Mentor

That is correct, PDE is partial differential equation. And the PDE (Maxwell's equations) we are talking about here is the easy part. The quantum mechanical stuff is even more challenging mathematically.

Yes. Superposition is essentially the same as saying you can get constructive and destructive interference.

I don't know exactly what you mean by the terms "complex wave" and "composite wave", but if you mean simply any wave function that is not a simple sinusoidal wave then, yes. In general the sum of two waves is a more complicated function than either wave individually.

7. Jan 28, 2008

### autek

I used the term complex and composite wave to indeed mean a single wave that is the result of the superposition of two or more waves that cannot be “easily” expressed in mathematical terms. Thanks again for taking the time to answer. It helped clear up a few questions for me.