# The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator

L. Essen, A. C. Gordon-Smith

## Abstract

The frequency of resonance of an evacuated cavity resonator in the form of a right circular cylinder is given by the formula f = v$_{0}\surd \left[\left(\frac{r}{\pi D}\right)^{2}+\left(\frac{n}{2L}\right)^{2}\right]$$\left[1-\frac{1}{2Q}\right]$, in which v$_{0}$ is the free-space velocity of electromagnetic waves, D and L are the internal diameter and length respectively of the cylinder, r is a constant for a particular mode of resonance, n is the number of half-wave-lengths in the resonator and Q is the quality factor. Assuming the validity of this equation the value of v$_{0}$ can be obtained from measured values of f, D, L and Q. A copper cylinder of diameter approximately 7$\cdot$4 cm. and length 8$\cdot$5 cm. was constructed with the greatest uniformity of diameter and squareness of end-faces and its dimensions were measured. The resonant frequencies for a number of different modes were measured and experiments were made to show that the effects on frequency of the coupling probes to the oscillator and detector were negligibly small. It was concluded from these measurements that the most favourable experimental conditions can be obtained for the E$_{010}$ and E$_{011}$ modes. Final measurements on these gave v$_{0}$ = 299,792 km./sec. The estimated maximum error of the result is 9 km./sec. (3 parts in 10$^{5}$). This is the error of a single measurement and, since most of the errors are not necessarily random, little is gained by making a large number of measurements. The value is 16 km./sec. greater than the recently determined values of the velocity of light, although the results are not in disagreement when the combined limits of accuracy are taken into account.