P. M. Kendig 245 
Table 13.1. Electroacoustical Relationships for Three Types of Piezoelectric 
Transducers 
Electroacoustical efficiency Square of equivalent noise pressure 
pora(1 —a)k? kT ([2bE tan 5(1 — k2)? + pw%a‘(1 — o) k2/v) 
Square of free -field 
voltage response 
Transducer 
shape 
a2(1 — 0) k? 
Sphere TOOT": 
# 2vbE tan 6(1 — k?)? + pworar(1 -o)k? moa'(1 — o)k? 2E¢ceo 
3_37,2 2y2 3)3)7,.2 2,2 
Cylinder po athe — kT ([2bE tan8(1 — k2)? + pw%a*1k?/v) ak. 
2vbE tan 8(1 — k2)* + pw°alk2 Toa [ke Eeo 
32,2 e252) 3.2), 72 2,2 
Senda || ———— Hb nO Gs lay pw et ee) 457k? 
vE tand(1—k;)° + pw°a’ bk ma’ whke Ee 
Since the square of the equivalent noise pressure varies inversely with the 
efficiency, it depends upon the same physical properties and transducer dimen- 
sions as does the efficiency. For all three transducer types, if the second term 
in the numerator is neglected, which may be done without materially affecting 
the results, it is seen that the square of the equivalent noise pressure varies 
inversely as the frequency. This assumes that tan is a constant for all fre- 
quencies, which is not necessarily true. Again, note that if tané approaches 
zero or if k, approaches unity, P? approaches the value 
2 
P? & e7e 
which is just the thermal-noise limit of the ocean. 
The last group of expressions presents the free-field voltage response in 
terms of the same parameters. It should be noted that 4, does not depend upon 
either the frequency or the medium; it does depend upon the modulus of elas- 
ticity, the dielectric constant, and the electromechanical coupling coefficient. 
It also depends upon some dimension of the transducer: for the hollow sphere 
and cylinder, it depends only upon the radius; and for the flat disk, it depends 
only upon the thickness. 
When using these relationships, any single consistent system of units may 
be used for the efficiency and the equivalent noise pressure. Since M, is usually 
expressed with a mixed system of units—namely, volts per microbar—a con- 
version factor must be used. For example, if the cgs-esu system is used, the 
results must be multiplied by 300 to obtain the usual volts per microbar. 
It seems worthwhile to re-emphasize the point that the free-field voltage 
response is definitely not an indication of the ability of a hydrophone to measure 
low-level signals, but that either the efficiency or the equivalent noise pressure 
is an essential indication of this ability. This is not to say that the free-field 
voltage response is unimportant, because low-level signals must be amplified 
to be measured. Now, the free-field voltage response depends upon the hydro- 
phone impedance, and this impedance, relative to the input impedance of the 
amplifier, is important if one is to take full advantage of the threshold sensi- 
