An important novel feature of the tethered sounding rocket experiment OEDIPUS A (Observations of Electric-field Distributions in the Ionospheric Plasma-A Unique Strategy) was its direct excitation and detection of electromagnetic waves on conductors in space plasmas. We present quantitative evidence about sheath waves excited in the ionosphere by a high-frequency transmitter on one end of the 1-km tether and detected by a synchronized reciever on the other end. An important characteristic of sheath waves is their sequence of sharply defined passbands and stop bands in the frequency range 0.1--5 MHz. The lowest passband is between 0.1 MHz and the plasma frequency near 2 MHz, the bandwidth where existing theory predicts sheath waves. Resonance fringes in this band have been scaled to determine the phase and group refractive indices of sheath waves. These agree reasonably well with the theory, considering the approximations therein. Passbands and stop bands observed in the range between 2 and 5 MHz are not expected on the basis of the current theory. In this range, band limits have clear signatures of the interaction of the tether fields with electrostatic cyclotron waves. Finite wire moment method modeling of the payload shows that in the low-frequency passband, RF coupling along the tether is increased by 20 dB over vacuum conditions. Similarly, isolation is greater than vacuum isolation in the stop bands. Because sheath waves at frequencies up to 2 MHz are guided efficiently along conductors in plasma, they are a significant design issue in the electromagnetic compatibility of avionics at frequencies up to HF on large metal space structures. ¿ American Geophysical Union 1995