Discriminating between the nearfield and the farfield of acoustic transducers

Measurements of the performance of acoustic transducers, as well as ordinary measurements made with the same, may require discriminating between the farfield, where the field is spherically divergent, and the complementary nearfield, where the field structure is more complicated. The problem is addressed for a planar circular piston projector, with uniform normal velocity distribution, mounted in an infinite planar rigid baffle. The inward-extrapolated farfield pressure amplitude pf is compared with the exact nearfield pressure amplitude pn, modeled by the Rayleigh integral, through the error 20 log |pf /pn|. Three sets of computations are performed for a piston with wavenumber-radius product ka = 10: normalized pressure amplitudes and error versus range at angles corresponding to beam pattern losses of 0, 10, 20, and 30 dB; error versus angle at three ranges, a(2)/λ, πa(2)/λ, and 10a(2)/λ, where λ is the wavelength; and range versus angle for each of two inward-bounded errors, 1 and 0.3 dB. By reciprocity, the results apply equally to the case of a baffled circular piston receiver with uniform sensitivity over the active surface. It is proposed that proximity criteria for measurements of fields associated with circular pistons be established by like modeling, and that a quality factor be assigned to measurements on the basis of computed errors.