Measure the speed of light with chocolate

The question

Can I measure the speed of light in my kitchen?

Learn just enough first

Look up what a standing wave is
Learn the wave equation: speed = frequency × wavelength

Kit

Microwave oven (check the label on the back for its frequency — usually 2450 MHz)
A large flat chocolate bar, or a plate of grated cheese or marshmallows
A ruler
A plate

My prediction

The accepted value is about 300,000 km per second. How close do I think a kitchen ruler can get?

Method

Take the turntable out so the food doesn't rotate.
Put the chocolate on an upside-down plate and heat it for about 15–20 seconds, until a few spots just start to melt.
Measure the distance between neighbouring melted spots, in metres.
Repeat with a fresh bar or a different spot, and average the results.

Safety: Don't run the microwave empty, and take the plate out with oven gloves — it can get hot.

Data

Trial	Distance between melted spots (m)
1
2
3

Result

The melted spots are the hot points of a standing wave, which sit half a wavelength apart. So the wavelength is twice the spot distance $d$, and:

$$ c = 2 \, d \, f $$

With $f = 2.45 \times 10^{9}$ Hz, a spot spacing of about 6 cm gives roughly $2.9 \times 10^{8}$ m/s. Compare my number with the accepted $2.998 \times 10^{8}$ m/s.

Explain it to a friend

Microwaves are light you can't see. Inside the oven they bounce back and forth and set up a pattern of hot and cold spots. Measure the spacing, multiply by the oven's frequency, and you've measured the speed of light.

New questions

Why are the hot spots exactly half a wavelength apart?
What limits my accuracy most — the ruler, or deciding where a spot really is?