In 4th generation nuclear reactors cooled with liquid sodium, argon microbubbles are present in the primary sodium. Due to the opacity of liquid sodium, acoustic control methods are chosen for operating inspections. However, this bubble presence greatly affects the acoustical properties of the medium. In bubbly liquids, nonlinear propagation can arise at very low amplitudes and therefore affect the viability of ultrasonic measurements. The spectroscopic measurement of the nonlinear parameter is therefore required to estimate the reliability of acoustics measurements. Moreover, adding nonlinear information to attenuations and celerity measurements could improve bubble distribution estimation and provide more reliability on very low void fractions measurements. A dynamic acoustic-elastic testing method is employed to measure the nonlinear parameter over a large bandwidth. Inversion of these measurements is performed with success.