A new radiation force balance method for measuring diverging piston source power in the frequency range 20-100 kHz: Theory and experimental verification.

The purpose of this work was to present the results of a theoretical and experimental study in which a new acoustic output power measurement method was developed for a strongly diverged ultrasonic beam (ka < 3, where k is the circular wave number and a is the radius of transducer) using acoustic radiation force. To the best of our knowledge, there is no acceptable and effective method to measure acoustic power P for diverging piston transducers from 20 kHz to 100 kHz in the range ka < 3, it is a unsolved problem acutely. In the study, we used radiation force balance (RFB) method with a novel concave semi-spherical absorbing target in far field to measure the acoustic power up to 54 W. Based on the phase inverse mirror-image model we developed and Bridge's product theorem, the axial radiation force F on the target was first calculated and measured. The maximum difference of the ratio r (=P/cF) between theoretic and experimental values was smaller than 5%, where c is speed of sound in water. The reproducibility test of acoustic power measurements using two independent methods showed that the measurement uncertainty evaluated less than 10% by the new RFB method was much smaller than that (30%) by the traditional acoustic pressure method in underwater acoustics. It is indicated that the new RFB method is a primary and effective method for acoustic power measurement at least up to 20 W for frequency range 20 kHz to 100 kHz. The similar method was extended to power measurement for the rectangular transducer. Based on this method a new primary method of hydrophone calibration was also developed.