SELF AND MUTUAL TIME-DEPENDENT INTERACTION FORCES BETWEEN ULTRASONIC TRANSDUCERS - APPLICATION TO THE COMPUTATION OF RADIATION IMPEDANCES

In this paper, diffraction theory is used to describe the self and mutual time-dependent interaction forces between ultrasonic transducers. This concept is interesting since it is equivalent, up to a temporal Fourier transform, to the radiation impedance. The formalism allows a description of self and mutual radiation impedances in terms of the aperture functions of the emitter and the receiver, and this description does not suppose that the transducers work in the piston mode. Then, the formalism is used to retrieve the well-known results about the radiation impedance of a circular piston. Finally, the mutual radiation impedance between two transducers is analyzed, and the particular case of small transducers compared to the wavelength is discussed. The results are similar to those obtained by Stepanishen and Pritchard [R. L. Pritchard, J. Acoust. Soc. Am. 32, 730-737 (1960); P. R. Stepanishen, ibid. 49, 283-292, 841-849 (1971)], except that the results here exhibit a correction term that increases the validity domain of the approximations.