54 



TESTING TECHNIQUE 



D/X 

 Figure 14. Spherical wave correction for circular piston. Correction to be added to measured response. 



The deviation from the inverse-square law may be and 

 treated as a correction. What one would like to meas- 

 ure is p„ as given by equation (43). Thus, the ratio 

 of the measured pressure to the desired result is 





sin ^(V« 2 + >' : 



(45) 



Substituting for r the usual symbol for testing dis- 

 tance d, and for a, i/ 2 the diameter of the piston D/2, 

 this equation becomes 



P_ 



P» 



8\d 



7rD- 



1,1 aWt+^ -<'):• (46) 



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 derivation 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-square law is valid for a 

 piston is given by 



d>^, 



A 



(47) 



d > 2L (48) 



where L is the longest dimension of the piston. 



5.4.5 Proximity Effect for Pistons: 



Directivity 



The 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 measurements, 

 the following criteria should essentially be met: 



d> 



L 2 



and 



d > 10L. 



(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 found 

 at distances in the inverse-square-law region. The 

 side lobes of the pattern appear higher than those for 

 long distances, and the minima separating the vari- 

 ous lobes begin to fill in. These effects are shown for 

 an extreme case in Figure 16, where testing distances 



