Radiation force on a spherical object in an axisymmetric wave field and its application to the calibration of high-frequency transducers

The general formulation for the radiation force on a spherical object in an axisymmetric acoustic field is provided. The sphere is described in general by three parameters: its density, compressional wave speed, and shear wave speed. Other types of spheres, including the rigid and immovable sphere and the infinitely soft sphere (void), are treated as limiting cases. Specialized formulations of the radiation force function are provided for several types of incident waves of common interest. A low-frequency expansion for each case is provided for comparison with results from the literature. Among the solutions provided are the scattering function of an elastic sphere in a focused acoustic field and the radiation force on the sphere. The radiation force function is used to calibrate high-frequency transducers. Experimental data are provided for a focused transducer for frequencies up to 10 MHz, where the size of the elastic sphere is comparable to or larger than the −3-dB beamwidth of the sound field.