Theoretical calculations were performed to investigate the ultrasonic properties of NiAl based ternary alloy NiAl-Cu. The interaction potential model approach has been used to measure the temperature dependent single crystal higher order elastic constants. Other acoustical parameters such as ultrasonic attenuation, Gruneisen numbers, acoustic coupling constants and relaxation time have been also calculated to discuss the acoustical properties insight the ternary alloys. Attention is given to analyze the ultrasonic wave propagation behavior at different temperatures for the alloy and is correlated with respect to the microstructural phenomena during the wave propagation and thermal behavior of the ternary alloy.An ultrasonic mechanism has been developed to correlate the temperature dependent ultrasonic propertieswith thermophysical properties particularlywith the thermal conductivity of the material. Results from the theoretical model calculations were found to be in good agreement with the experimentalmeasurements on the alloy.