18 Lecture 1 
of about 1 w/em? is required to produce cavitation in sea water. This implies that 
the inherent tensile strength of sea water is about 0.8 atm. The relationship be- 
tween intensity to produce cavitation I (w /cm*) and the depth of the projector in 
feet H is therefore of the type 
ts 03(4 + 1.8) (18) 
If such a relation is reliable, the cavitation limit is raised to about 7 w/cm? at a 
depth of 100 ft. No published work on the effect of depth or hydrostatic pressure 
on the cavitation limit has been found; however, the limit of 7 w/em? at 100 ft 
is in agreement with measurements carried out by the Naval Research Estab- 
lishment which will be described later. 
The above discussion of cavitation has been oversimplified; the presence of 
dissolved gases, impurity nuclei, temperature, andthe pulse length of the acoustic 
signal will all affect the intensity at which cavitation is initiated. The radiating 
face of the transducer can also affect the inception of cavitation and “hot spots" 
can occur at levels considerably below the average level of cavitation. Further 
studies on cavitation as applied to transducers are desirable. 
Although cavitation is the ultimate factor limiting the power output, many 
transducers reach their maximum power-handling capacity before the onset of 
Cavitation even at shallow depths. Crystal piezoelectric transducers of the ADP 
and quartz type are inherently high-impedance devices requiring very high 
voltages to excite them to high powers. The limiting factor in this class of trans- 
ducers is not cavitation but the voltage at which breakdown occurs across the sur- 
face of the crystals. 
The important factors in the barium titanate compound-bar type of element 
are considered to be: (a) the dynamic strength of the element and (b) the heating 
associated with the dielectric and mechanical losses. The dielectric losses are 
kept as low as possible by using a specially developed barium titanate composi- 
tion with additions of cobalt [12]. The mechanical losses are not a problem since 
the elements have a high motional-to-acoustic conversion efficiency. The power- 
handling capacity therefore appears to be limited by the dynamic strength of the 
element. 
Tests were carried out on a 10-kcps transducer containing four elements 
at a depth of about 100 ft with 75-msec sinusoidal pulses at a repetition rate of 
1 per sec. Figures 1.10 and 1.11 and Table 1.1JI summarize the results. It is evi- 
dent that the change in admittance and the decrease in efficiency is due to an in- 
crease in the internal mechanical losses. An examination of the conductance vs 
frequency curves shows that the clamped value of conductance, which is propor- 
tional to dielectric loss, changes little with increasing driving voltage as was 
expected with the barium titanate composition used. 
The elements fractured at about 6 w/cm?, It can be readily calculated that 
at this peak power output, the stress at the node is about 670 psi. Tensile-strength 
tests showed that the static strength was about 3000 psi or four times the dynamic 
strength. This discrepancy has never been satisfactorily explained. Care was 
taken to eliminate transients, and fatigue is not a satisfactory explanation since 
one pulse at the high level would cause the element to break. The fracture took 
