# Labs from Chicago, Fall 1992 : Radio Pulse Dispersion.

Dr. Jim Sweitzer
Labs written for the CARA Space Explorers, Fall 1992; it was due at the Yerkes Winter Institute 1992.

This is meant to be handed out to the students.

In this activity we're going to investigate what happens as the radio waves from a sferic travel along a magnetospheric duct to a radio on the other side of the world. You already know from our discussion that a whistler is the result, but let's now see why that is.

When electromagnetic waves travel in empty space, they all travel at the same speed, no matter what the frequency. When they travel in matter, it's another thing. You remember using a prism to break up light into its different colors (same thing as frequencies). Well, that happens because different colors travel at different speeds as they travel through glass. The details depend on how the light interacts with the atoms in the glass.

Radio waves that we have experience with travel through plasmas. A plasma is just like a gas, except that some of the electrons have been stripped off the atoms and molecules. A plasma, therefore, conducts electricity something like a metal yet is like a gas. Fluorescent tubes and the sun are two good examples of plasmas. Radio waves interact strongly with the plasmas surrounding the earth in the ionosphere and magnetosphere. And radio waves of different frequencies travel at different speeds, just like visible light in glass.

The speed (V)of a radio wave of frequency F in a plasma is something like this:

V = Constant x F

Let's let the constant be a number we'll call k (we'll solve for it), let the frequency (F) be in kilohertz, and the speed in kilometers per second. Then our equation becomes:

V(km/s)=k x F(KHz) For the sake of argument, let's say that from the audio tapes we listened to, we found that it took 0.5 seconds for the first frequency (10kHz to reach us). You should have solved for the path length for the magnetospheric duct from last week. That answer was:

_________________________________km.

1. Now, given this information, figure out what the constant must be in the equation. Show your work below and write down the formula with the correct constant.

2. Suppose the sferic that created the whistler began by emitting radio waves of all wavelengths between 100 Hz and 10 kHz. Pick ten representative frequencies in this range and fill in the following table. Don't forget to use the constant that you just determined.

```Frequency (kHz)	Speed (km/s)	Time to travel magnetospheric duct (s)

```
3. Now, graph frequency versus travel time on the plot below. First you'll have to choose and label axes and scales that make sense. The zero in time is set by the sferic.

[Graph paper doesn't convert to hypertext!]

4. Which frequencies (high or low) arrive first? __________________

Which frequencies arrive last?__________________

5. Suppose there were no dispersion of the radio waves generated by the sferic, yet you were still on the other end of the earth listening to these radio waves. Make your own plot below, similar to above, but with out dispersion and show what would happen. Be sure and show that time zero starts with the initial sferic. Also assume that the speed of the radio waves is the same as it would be for a 5 kHz wave in the preceding problem.

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