Transverse electromagnetic oscillations in a gyrotropic plasma exhibit Landau damping when the wave is not monochromatic. The dependence of the damping on the equilibrium distribution and the boundary (or initial) values is investigated. The resulting dispersion relation is interpreted by examining the response of a single free electron to an incident wave. It is shown that the damping mechanism is associated with the Doppler shift caused by the thermal distribution, so that some particles are in cyclotron resonance for any laboratory frequency. The correlation of whistler data with this complex dispersion relation can be used to evaluate electron temperatures at several earth radii; a specific numerical example givesT≈ 105°K atR≈ 4Re(geocentric).