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

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 [Formula: see text]. 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 , [Formula: see text] for membrane hydrophones far exceeds that for needle hydrophones at low frequencies (e.g., < 4 MHz when [Formula: see text]). This empirical model for [Formula: see text] 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.