Accuracy of a Microwave Resonant Cavity Measurement of the Velocity of Light

Abstract

Most of the problems involved in a measurement of the velocity of light by a microwave resonant cavity are discussed briefly on the basis of work reported elsewhere. A more nearly complete theoretical analysis of the effects of the cavity-surface impedance is given. In general, the surface reactance and resistance must both be known to relate the measured resonant frequency to the normal-mode frequency. This problem limits the accuracy of the experiment to an uncertainty of no less than about 2 parts in 10 6 . The formal requirements for reducing this uncertainty are stated, but no experiment is suggested.New and more accurate measurements were made of the volume change on melting of N2 up to 3500 kg/cm 2 . Liquid density and thermal expansion were also studied along the melting curve. A lowpressure metering system was used throughout. The AV m data were fitted to the empirical equation, AV m = A -B logio(.P+C), with success. Combination of this equation with our previously reported melting equation yields expressions for AS and AH of melting useful up to 3500 kg/cm 2 .

Refractive-index gas thermometry

“…gold plating on a steel shell) to increase its conductivity and to inhibit corrosion. If the plating is less than several penetration layers thick, we expect Δ f m ≠ g m (Janney 1957, Tischer 1976). Surface roughness increases both Δ f m and g m (Tischer 1976, Hernandez et al 1986).…”

RF measurements of the speed of light

“…The dependence of c on D can be suppressed so that the uncertainty in the diameter has a negligible effect on the accuracy of c. A cavity incorporating this concept has been described by Stroke [24]. However, Janney [25] has derived a more exact frequency correction of the form wherefis the actual resonant frequency,f, is the theoretical frequency of normal mode a, X is the surface reactance, and R is the surface resistance. This correction reduces to the one in (9) if X = R .…”