140 Lecture 9 
namely, 2 to 5 w/em’. If additional cooling is used, up to 15 w/cm? may be 
reached. The reason for the low output of the barium titanates is the internal 
heating of the transducer by mechanical and dielectric losses. At high input 
power, the temperature of the transducer may exceed the Curie temperature. 
Pulse modulation permits somewhat higher peak sound intensities because 
of the smaller mean output. With quartz, values of up to 500 w/cm? (at 1.5 Mcps) 
and with barium titanate about 20 w/cm? are reported in the literature [2]. 
For frequencies below 200 kcps, magnetostrictive transducers are very often 
used. These are, in most cases, composed of superficially oxidized nickel 
sheets. In spite of the rugged design of these transducers, the maximum in- 
tensity is limited to about 7 to 16 w/cm? by friction losses between the sheets 
and by the AE effect. 
The new piezomagnetic ferrites (nickel—copper—cobalt ferrites, "Ferrox- 
dure") developed by Philips, Eindhoven, can generate maximum intensities of 
3 to 6 w/cm? in continuous operation [3]. 
In order to concentrate high energies into very limited space, it is much 
more efficient to use cylindrical or even spherical shells as radiators. The first 
to propose such radiators was Johannes Gruetzmacher [4], who used a concave 
quartz shell with a resonant frequency of several hundred kcps. If the point of 
convergence is near the surface of the liquid, the well-known bubbling water or 
oil spring caused by Langevin's radiation pressure is observed. The height of 
the spring is an indication of the extreme energy densities. The attainable power 
at the focus of the quartz radiator is estimated to be of the order of 20 kw/cm?. 
For barium titanate shells, 300 w/cm?* was reported. Even if cavitation is pre- 
vented (e.g., by applying excess static pressure), a natural limit is set for the 
attainable energy densities because the energy is prevented from focusing by 
diffraction, and also because nonlinear strains in the transmitting medium in- 
crease the absorption. 
In the lower frequency ranges often many small sound-radiating elements 
are arranged mosaiclike on a large spherical surface (A. Williams). Such in- 
struments are manufactured with barium titanate transducers by the Clevite 
Company in Cleveland, Ohio. 
L. D. Rozenberg and M. G. Sirotyuk [5] have proposed an especially interesting 
construction of this kind. They have used a spherical aluminum shell with an 
inner radius of 314 mm; the thickness of the shell is exactly equal to \/2 at the 
operating frequency of 500 kcps. Distributed over the outer surface of the shell 
are 160 to 200 spherically polished quartz thickness vibrators immersed in oil. 
The attainable intensity in the focus area is 60 to 70 kw/cm? with peak pressures 
of up to 500 atm. 
An arrangement consisting of 21 magnetostrictive transducers (14.6 kcps) 
was used in the III Physikalisches Institut of the University of Gottingen for the 
investigation of cavitation in liquids in the absence of disturbing boundary layers 
{6]. 
9.1.2, Pulse Transducers 
The sinusoidal vibration of electroacoustic transducers may be pulse-modu- 
lated in order to keep the time average of the power small. This is facilitated 
by a very simple method used with magnetostrictive and barium titanate trans- 
