The recovery of petrochemical and geothermal resources requires extensive drilling of wells to increasingly greater depths. Real-time collection and telemetry of data about the drilling process while it occurs thousands of feet below the surface is an effective way of improving the efficiency of drilling operations. Unfortunately, due to hostile down-hole environments, telemetry of this data is an extremely difficult problem. Currently, commercial systems transmit data to the surface by producing pressure pulses within the portion of the drilling mud enclosed in the hollow steel drill string. Transmission rates are between 2 and 4 data bits per second. Any system capable of raising data rates without increasing the complexity of the drilling process will have significant economic impact. One alternative system is based upon acoustical carrier waves generated within the drill string itself. If developed, this method would accommodate data rates up to 100 bits per second. Unfortunately, the drill string is a periodic structure of pipe and threaded tool joints, the transmission characteristics are very complex and exhibit a banded and dispersive structure. Over the past 40 years, attempts to field systems based upon this transmission method have resulted in little success. This article examines this acoustical transmission problem in great detail. The basic principles of acoustic wave propagation in the periodic structure of the drill string are examined through theory, laboratory experiment, and field test. The results indicate the existence of frequency bands that are virtually free of attenuation and suitable for data transmission at high bit rates.