Speed of Light

Radio Waves

Equipment: You will need

$\bullet$ A compass

$\bullet$ A Map

$\bullet$ An FM radio

$\bullet$ A meterstick, or a tape measure.

$\bullet$ masking tape
 

Theory: This determination of the speed of radio waves makes use of the fact that ones' body strongly scatters FM radio waves. The scattered wave then can interfere with the incident wave at the radio receiver. By logging the distances between receiver and body where destructive interference occurs and correcting for some systematic effects (phase shift at the scatter, and phase differences across the incident wave front) and using the frequency of the radio station it is possible to estimate the velocity of the radio wave.
 

Procedure:
 

1.) Put the radio on the floor of a big open hallway. Tune into a distant, weak FM radio signal (preferably Pittsburgh or Cleveland). Listen for station identification and locate on the map roughly the origin of the radio waves. Estimate how many degrees away from true north (or true south) the heading to the station would be and use a compass to lay out a piece of masking tape along a direction roughly toward the station through the radio.
 

2.) Make sure the antenna on the radio is fully extended and straight up. Walk around the radio, and listen for spots to stand where the station drops out. Mark those spots. Find a few of them that lie along lines perpendicular to the original masking tape line.
 

HINT: You need to find about 4 spots at varying distances. Use only one person for this part, and try not to have anyone else moving around as that may throw things off. If the station that you have chosen is too strong and you cannot find enough places at which the signal drops out you need to find another station, A station that works well in this area is ______________________
 

3.) Now measure (along the ground) the distance between the dead spot and the radio's antenna. Measure this distance for all the dead spots along a line, roughly, perpendicular to the original masking tape line. Compute differences between these distances among themselves among each set of lined-up dead spots.
 

Analysis: FM radio waves are scattered by your body. Some of that scattered wave travels back toward the radio. The radio responds only to the sum of the incident wave from the radio station and the scattered wave from your body. The phase of the scattered wave and the incident wave differ by two terms. One is the intrinsic phase shift due to the electrical properties of your body. The other phase difference is due to the fact that the scattered wave has travelled a different distance  to the radio receiver than has the incident wave from the station.

We can eliminate the effect of the intrinsic phase shift by always computing phase differences (by taking the differences of the distances) between two drop out spots. Further, we can eliminate the second difference (different distance from the transmitter) by only comparing drop outs along roughly the line perpendicular to the direction to the radio station.

Drop outs occur when the scattered wave from the body destructively interferes with the wave from the radio station. If one of the line-up drop outs is a distance $d_1$ from the radio antenna and another is a distance $d_2$, then each of these are (up to an overall phase) an odd multiple of half wavelengths off from the incident wave. That means that the difference $d_1-d_2$ is expected to be a multiple of the wavelength (note that the overall phase cancels out!).

Thus writing out a few of these distance differences indicates which are 0, 1 and 2 wavelengths of the incident wave. From that the wavelength can be determined and thus the speed of light through

$$c = \lambda f$$

where $\lambda$ is the wavelength and $f$ is the frequency in cycles per second (Hertz). A Megahertz is $10^6$ Hertz.

This experiment typically yields a 30 % estimate of the speed of light.