. Basic methods for the calibration of sonar equipment. 54 TESTING TECHNIQUE. D/X Figure 14. Spherical wave coneclioii for circular piston. Correction to be added (o meastiied response. The deviation from the inverse-square law may be and treated as a correction. What one would like to meas- ure is pâ as given by equation (43). Thus, the ratio of the mcasiued pressure to the desired result is p^^2Ar sin -(V"- + >'â (45) Substituting for r the usual s\nibol for testing dis- tance d, and for a, 1/9 the diameter of the piston Dj2, this equation becomes Sxd ttD- -aWt+^'^'-^OI- ^''^ A chart
. Basic methods for the calibration of sonar equipment. 54 TESTING TECHNIQUE. D/X Figure 14. Spherical wave coneclioii for circular piston. Correction to be added (o meastiied response. The deviation from the inverse-square law may be and treated as a correction. What one would like to meas- ure is pâ as given by equation (43). Thus, the ratio of the mcasiued pressure to the desired result is p^^2Ar sin -(V"- + >'â (45) Substituting for r the usual s\nibol for testing dis- tance d, and for a, 1/9 the diameter of the piston Dj2, this equation becomes Sxd ttD- -aWt+^'^'-^OI- ^''^ A chart is given in Figure 14 showing the corrections in db to be added to the measured values. A similar analysis may be made for a line transducer. The cor- rections for this instrument are shown in Figure 15 where L, the length of the line, replaces D. While the preceding deri\ati()n is for a circular piston, essentially the same limit holds for a piston of any shape if the diameter of the piston is replaced by a characteristic linear dimension for the shape under consideration. A general criterion for the domain where the inverse-scjuare law is valid for a piston is given by d>^, A (47) d >2L (48) wliere L is the longest dimension of the piston. Proximity Effect for Pistons: Directivity 14ie effect of proximity on the directivity pattern of a transducer is not as amenable to calculation as the effect on the axial response. To avoid appreciable effect due to proximity in directivity measinements, the following criteria should essentially be met: d> L-' and d > lOL. (49) Qualitatively, the effects on directivity patterns of measuring at a closer distance than prescribed by the above criteria are known. Measurements show that the measured beam width is broader than that foimd at distances in the in\erse-square-law region. Ihe side lobes of the pattern appear higher than those for long distances, and the minima separating the vari- ous lobes begin to fdl in. These
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