6 Lecture 1 
in the sense that they can be used for either purpose. Interesting possibilities, 
such as hydrodynamic oscillators, will not be considered. The principles of elec- 
troacoustic conversion will be only very briefly discussed since these are covered 
in well-known texts [1]. Piezoelectricity, electrostriction, and magnetostriction 
are the most widely used phenomena in underwater acoustic transducers, and the 
advantages and disadvantages of materials exhibiting these phenomena will be 
discussed. Much of the foregoing is covered inthe literature but a gap exists be- 
tween the fundamental principles and the application of these principles to prac- 
tical transducers. About one-half of the paper is devoted to an examination of the 
design oftwo typical transducers, a multielement compound-bar projector unit and 
a hydrophone designed for operation deep in the ocean. 
1.2, ELECTROACOUSTIC CONVERSION PRINCIPLES 
Examining all the theoretically possible direct methods of converting elec- 
trical to acoustic energy means determining the possible forces that electrical 
and magnetic energy exert on matter. 
Basically the force effects due to an electric field are dependent on the fact 
that a force F is exerted on an electric charge q in an electric field E given by 
the expression F = gE. This fundamental relation is onlytrue if q can be regarded 
as a point charge. Such conditions do approximately exist in crystal lattices; 
and if the ions in the lattice move easily relative to one another, the crystal will 
deform on the application ofanelectric field. Conversely if a mechanical force is 
applied to such a crystal and the lattice deforms, electric charges appear on the 
surface of the crystal. This phenomenon is called piezoelectricity and has been 
widely used in underwater transducers. However, due to the anisotropy inherent 
in their crystal structure, the relationship between the electric field and mechani- 
cal stress in piezoelectric crystals is not simple, and in the general case, not 
only normal but also shear stresses are generated. The stresses can be repre- 
sented by six equations of the type: 
T,,=€11E, + e21 Ey +e3 Ez 
Tyy =@12 Ex + em Ey + €32 Ez 
Tzz = €13 E, + €23 Ey + 33 E, (1) 
Tyz = 14 Ex + Cm Ey + ey, Ez 
Tz, = © 1sEy + C95 Ey + €35 E, 
Try = @16 Ey ters Ey peas Es 
where E;, E,, and E, are the electric field strength components;T,, , Ty, , and 
T,, the normal stresses; T,,, T,,, and T,,, the shear stresses; and e,;,, the piezo- 
electric constants, which are different for the various piezoelectric materials. 
Some simplification is possible by grinding plates fromthe crystals at particular 
orientations to the crystallographic axes. In quartz, for example, all the e co- 
efficients are zero with the exception Of e41, e495 ey4 eos, ANd ex. If a rectangular 
plate is ground from the crystal, with the planes of the plate perpendicular to 
the coordinate axes of quartz, and a voltage V is applied in the x direction, the 
equations representing the stresses are reduced to three. Moreover, if our 
