A full bandwidth calibrator for a sound pressure and particle velocity sensor

In literature it is shown that it is possible to calibrate a sound pressure and a particle velocity sensor in the free field at higher frequencies. This is done by calculating the acoustic impedance at a certain distance of a spherical loudspeaker. If the sound pressure is measured with a reference microphone the particle velocity can be calculated. At lower frequencies this setup does not work. The pressure microphone is calibrated by comparing its response with the reference microphone. In this paper the method is extended for lower frequencies by placing the reference microphone in the loudspeaker. At low frequencies the sound pressure in the sphere is proportional to the loudspeaker movement. If the movement is known, the particle velocity in front the loudspeaker can be derived