42 



TESTING TECHNIQUE 



SURFACE 



so that 



BOTTOM 



Ficure 3. Geometry of reflection interference in calibra- 

 tion tests. 



with the result that 



wD 



R - = 

 p 





27, 



(f 



2/i 



Vrf- + 4/i 



0' 



tt/J 

 A 



2/t 



Vd 2 + 4/v- _ 



(12) 



The term D is the diameter of the piston, A the wave 

 length, and 7i(v) the Bessel function of unit order. 

 For a line source of length L suspended vertically, 





in i— sin J 



sin 9 



(13) 



«r 



i n ^ . 2/t \ 



11 \ A ' \/d- + 4/i-V 



2/i 



Vd" + 4/)-' _ 



(14) 



Since the side lobes for a circular piston and for a 

 line are of minor importance in the consideration of 

 reflections, R, h R,,, and R t may be given approxi- 

 mately (provided h /d is not too large) by the expres- 

 sions 



«.'--Kf) ! (3^> 



(10) 

 (15) 

 (16) 



The reflected intensity reaching the receiver versus 

 the intensity of the direct wave is then given in db by 



where a = 1 for a pressure-gradient receiver, a = 

 y 4 (-7rD/\)- for a circular piston, and a = y 3 (irL/\) 2 

 for a line. This equation is plotted in Figure 4. It is 

 seen that, for reducing the effect of reflections, a 

 piston is more satisfactory than a line whose length is 

 equal to the diameter of the piston. At low fre- 

 quencies, however, where A becomes large, both a line 



h 

 d 



Ficure 4. Surface reflected intensity versus direct intensity for directional sources, h = depth, d = testing distance. 

 For dipole source «= 1; for circular piston source a = i/ 4 {irD/\f, D = diameter of piston, X = wavelength; for line 

 source suspended vertically, a = i/ 3 (*L'/\)*, L = length of line. 



