D. Schofield 21 
where p = a/b and a and b are the internal and external radii of the shell, respec- 
tively. For a thin shell p +1 and the equation reduces to 
—=-b §3 
The sensitivity of a thin spherical-shell hydrophone is therefore directly pro- 
portional to the diameter. 
The sensitivity as a function of frequency should be constant until the sphere 
is no longer a small fraction of a wavelength, say \/8. When this occurs, there 
will be a phase difference across the sphere and cancellation will cause a reduc - 
tion in the sensitivity. 
Resonance occurs in air at a frequency given by 
vesall eel (20) 
7b | 2p (1 - 0) 
where Y,, is the elastic-stiffness constant, o is the Poisson ratio, andp is the 
density of ceramic. Only for very thin-walled spherical shells is the resonant 
frequency appreciably lower in water than in air. 
Spherical shells have been assembled by cementing together carefully selected 
hemispheres with a nonconducting adhesive such as an epoxy resin. The lead to 
the inner electrode passes through a ceramic-to-metal seal in the shell. The 
hydrophone is waterproofed by several dippings in a liquid neoprene solution. 
The sensitivity as a function of frequency is given in Fig. 1.13 for a 3-in. 
diameter 1) -in. wall thickness barium titanate sphere. The experimental sensi- 
tivity is in good agreement with the theoretical value of 17 pvolt/ubar. As 
suggested previously, the sensitivity is flat with frequency until the sphere is 
about A/8, i.e., at about 3 kcps. Theoretically, a spherical transducer should 
be omnidirectional at all frequencies but, since the practical units are not perfect 
spheres, deviations from true omnidirectionality occur in the neighborhood of 
resonance and at higher frequencies. At resonance the directivity pattern is omni- 
directional to about 1 db and at 50 kcps to about + 2 db. 
100 T a mmnns T i amrnan T 
a 
1 jaan 
pt VOLTS /2 BAR 
10 
FREQUENCY KC/S 
Fig. 1.13. Hydrophone sensitivity vs frequency for a 3-in. diameter and 
V4-in, wall barium titanate sphere. 
