Directivity and Frequency-Dependent Effective Sensitive Element Size of Membrane Hydrophones: Theory Versus Experiment

It is important to know hydrophone frequency-dependent effective sensitive element size in order to account for spatial averaging artifacts in acoustic output measurements. Frequency-dependent effective sensitive element size may be obtained from hydrophone directivity measurements. Directivity was measured at 1, 2, 3, 4, 6, 8, and 10 MHz from ±60° in two orthogonal planes for eight membrane hydrophones with nominal geometrical sensitive element radii (a
_g
) ranging from 100 to 500 μm. The mean precision of directivity measurements (obtained from four repeated measurements at each frequency and angle) averaged over all frequencies, angles, and hydrophones was 5.8%. Frequency-dependent effective hydrophone sensitive element radii a
_eff
(f) were estimated by fitting the theoretical directional response for a disk receiver to directivity measurements using the sensitive element radius (a) as an adjustable parameter. For the eight hydrophones in aggregate, the relative difference between effective and geometrical sensitive element radii, (a
_eff
- a
_g
)/a
_g
, was fit to C/(ka
_g
)
ⁿ
, where k = 2π/λ and λ = wavelength. The functional fit yielded C = 1.89 and n = 1.36. The root mean square difference between the data and the model was 34%. It was shown that for a given value for a
_g
, a
_eff
(f) for membrane hydrophones far exceeds that for needle hydrophones at low frequencies (e.g., c4 MHz when a
_g
= 100 μm). This empirical model for a
_eff
(f) provides information required for the compensation of spatial averaging artifacts in acoustic output measurements and is useful for choosing an appropriate sensitive element size for a given experiment.