  We describe an undergraduate laboratory that combines an accurate measurement
of the speed of light, a fundamental investigation of a basic laser system, and
a nontrivial use of statistical analysis. Students grapple with the existence
of longitudinal modes in a laser cavity as they change the cavity length of an
adjustable-cavity HeNe laser and tune the cavity to produce lasing in the
TEM$_{00}$ mode. For appropriate laser cavity lengths, the laser gain curve of
a HeNe laser allows simultaneous operation of multiple longitudinal modes. The
difference frequency between the modes is measured using a self-heterodyne
detection with a diode photodetector and a radio frequency spectrum analyzer.
Asymmetric effects due to frequency pushing and frequency pulling, as well as
transverse modes, are minimized by simultaneously monitoring and adjusting the
mode structure as viewed with a Fabry-Perot interferometer. The frequency
spacing of longitudinal modes is proportional to the inverse of the cavity
length with a proportionality constant equal to half the speed of light. By
changing the length of the cavity, without changing the path length within the
HeNe gas, the speed of light in air can be measured to be ($2.9972 \pm0.0002)
\times 10^{8}$ m/s, which is to high enough precision to distinguish between
the speed of light in air and that in a vacuum.
