Non-intrusive acoustic instruments that measure fluid velocity and temperature have been restricted to low subsonic Mach number applications due to increased complexities associated with acoustic refraction, low signal-to-noise ratios, and a limited range of practical applications. In the current work, the use of acoustics for non-intrusive flow monitoring in compressible flows is explored and a novel sonic anemometry and thermometry (SAT) technique is developed. Using multiple arrangements of SAT equipment, a compressible acoustic tomography technique was also developed to resolve flow non-uniformities. Three validation experiments were used to investigate the novel SAT technique performance, and a fourth validation experiment was used to explore compressible flow tomography capabilities. In the first experiment, an unheated jet was used to verify that the acoustic technique could measure fluid velocities in high subsonic Mach number flows. The application demonstrated velocity root mean square (RMS) errors of 9 m/s in unheated jet flows up to Mach 0.83. Next, a heated jet facility was used to assess the impact of fluid temperature on measurement accuracy. Using jet Mach numbers up to 0.7 and total temperatures up to 700 K, RMS velocity and static temperature errors up to 8.5 m/s (2.4% of maximum jet velocity) and 23.3 K (3.3% of total temperature) were observed. Finally, the acoustic technique was implemented at the exhaust of a JT15D-1A turbofan engine to investigate technique sensitivity to bypass engine conditions. A mass flow rate and thrust estimation approach was developed and RMS errors of 1.1 kg/s and 200 N were observed in conditions up to an exhaust Mach number of 0.48. Since modern acoustic tomography techniques require an incompressible flow assumption for velocity detection, advancements were made to extend acoustic tomography methods to compressible flow scenarios for the final experiment. The approach was tested in the heated jet operating at Mach 0.48 and 0.72 (total temperature of 675 K, approximately 2.25 times the ambient) and numerical simulations were used to identify technique sensitivity to input variables and system design. This research marks the first time an acoustic method has been used to estimate compressible flow velocities and temperatures. / Ph. D.