Re: is it valid to use a microwave oven to estimate the speed of light?

Greetings Sue:

References:

1. S. Ramo, J. R. Whinnery, T. Van Duzer,
Fields and Waves in Communication Electronics, John Wiley & Sons, 1967

2.Math and Physics Applets
http://www.falstad.com/math physics.html

3. Mad Science Archives Question: What is a waveguide?
http://www.madsci.org/posts/archives/1997- 08/869860698.Ot.r.html

4. Mad Science Archives Question : When waves collide do both kinds
of interference occur?
http://www.madsci.org/posts/archives/1997- 03/853194471.Ph.r.html

5. Mad Science Archives Question : Measuring the characteristics of photons
in confined spaces.
http://www.madsci.org/posts/archives/2003- 12/1072272975.Ph.r.html

Thank you for your very interesting question. Your intuition is correct, there
are three dimensional (3D) aspects to Electromagnetic (EM) waves in a rectangular
microwave oven. The standing waves of EM power are somewhat similar to sound
waves in musical instruments; however, the details of the EM standing waves are
very complex. Fortunately, Reference 2 is an awesome web site where you can
visualize these standing waves in time. We call the rectangular box of the oven
a resonator or cavity and the pattern of the EM standing waves we call Modes.
These modes are located throughout the volume of the oven and spaced one half
wavelength apart in 3D. (Note this is only true for a rectangular cavity and
not for other volumes such as cylinders and spheres etc.)

Wave guiding structures.

During the 1930s, while working at the Bell Telephone Laboratories (BTL),
Dr. George Southworth discovered a new form of radio frequency transmission line
that he called Waveguides. Waveguides are a far more efficient transmission line
at microwave frequencies, compared to coaxial cable transmission lines, for
transmitting microwave power to and from transmitters, receivers and antennas. I
have discussed waveguides in more detail in Reference 3.

A microwave power source, a Magnetron in the case of a microwave oven, can be
connected to a small 1/4 wave long wire or a loop antenna inserted into the end of
a rectangular metallic waveguide. The antenna converts the energy of moving
electrons (electrical current) into photons. The photons produce EM waves in the
waveguide. A microwave oven forms a rectangular waveguide resonator (cavity) that
is several wavelengths long in each dimension X, Y, and Z. Thus a complex 3D
standing wave pattern is generated in the cavity and the pattern is defined by
the Mode structure.

Depending on the design of the coupling antenna, there are many different mode
structures that can be generated in a cavity. In this discussion I will use the
most simple mode structure as an example for it is similar, but not identical,
to the other possible mode patterns. The modes that I will use are called the
Transverse Electrical (TE) field modes. Depending on the oven design
it is also possible to excite Transverse Magnetic (TM) field modes which
I will not discuss.

The dimensions of my microwave oven are 20 x 20 x 10 inches high
(50.8 x 50.8 x 25.4 cm). The microwave oven frequency is 2.4 Gigahertz
(2.4 billion cycles per second) and the wavelength in free space is 4.92 inches
(12.5 cm). Thus my oven is about 8 x 8 x 4 one half wavelengths in size. Thus one
TE mode that could be excited in my oven would be TE (8,8,4). Thus there would
be 8 * 8 * 4 = 256 power modes distributed through out the oven volume and along
the oven floor we would have 8 * 8 = 16 power modes in a 8 by 8 pattern.

The Math and Physics Applets in Reference 2 only goes up to TE (4,4,4)
modes so it displays what would be a very small microwave oven; however, it is
similar to a larger oven, but with fewer power modes.

EM waves have a magnetic field that is orthogonal (90 degrees) to the electric
field and you will see that the magnetic field is minimum when the electrical
field is maximum and vice versa.

Using the Electrodynamics Cavity Modes Applet

1.Address the Math and Physics web site in Reference 2.

2. Scroll down to the Electrodynamics section.

3. Launch the Cavity Modes (Electromagnetic waves in a 3D rectangular cavity)
Applette. Be patient this will take a number of seconds to load.

You will notice the coordinate system of the display in the top right hand side of the
control pannel with fields in the X direction displayed in red, fields
in the Y direction displayed in green and fields in the z direction displayed in blue.

At the bottom of the display you will see 9 grids, each little grid square
represents a different mode. The top 4 grids are the TE modes and the bottom 5
grids are the TM modes. Place your mouse on the little green square on the top
left of the fist grid and it should read Selected Mode = TE (1,0,1) .

4. Click on the Clear button on the top right of the control pannel display
to clear the selected mode.
5. Place your mouse on the bottom right square of the right most grid in the top
row. The display should read Selected Mode = TE (4,4,4).

6. Click on the TE (4,4,4) mode square and the display should show the red and
green electric field power distribution which pulses between zero and maximum each
one half cycle of the microwave signal. You may want to increase the brightness in
the control board on the left of the display.

7. To see the magnetic fields in the blue direction in the cavity find the
Show Electric Field box on the right hand control panel. Click on the down arrow
and select Show Both Fields.

You should now see two displays the left showing the red and green electric
fields and the right showing the blue magnetic fiends. Note the blue magnetic
fields are out of phase with the electric fields. If you try to show all three
fields on the same display the colors become to mixed to distinguish what is
going on.

Discussion

The display shows how power modes are distributed within the cavity volume and
shows the distribution along the cavity bottom where you place the chocolate chips, or
temperature sensitive paper or what ever to see the power pattern. While this is
a simple and interesting demonstration of how one might try to measure the speed
of light, it is not very accurate. First, the ovens are not perfect cavities as
is assumed in the Applets. If the oven dimensions are not exactly increments of
one half wave, the mode pattern becomes smeared. Also, for reasons to complex to
discuss here, the wavelength of an electromagnetic wave confined in a metal box
is not the same as the wavelength is in free space. The difference depends on the
mode that is excited and how large the oven volume is in wavelengths. In the box
resonator,for well known reasons, the speed of propagation of the EM wave would
not be equal to the speed of light in a vacuum. Also measuring the distance between
the zero (null) power points in a standing wave is much more accurate that trying
to measure the distance between rounded points of maximum power where the chocolate
chips melt. However, students seem to want to try all sorts of experiments in
microwave oves as indicated in the Mad Science Archives.

If you are interested in more detailed aspects of your problem see my answers to
similar questions in the Mad Science Archives that I have referenced.

Best regards Your Mad Scientist
Adrian Popa