D. Schofield 15 
It has already been stated that for maximum bandwidth the practical problem 
is to achieve the condition 0,,~0, . Themechanical 0 can be calculated from the 
equation 
_ Wo Me 
2 (17) 
where M, is the effective mass of the element and can be calculated from kinetic 
energy considerations, poc, is the characteristic impedance of sea water, 4 is 
the effective radiating area, and wo is the resonant angular frequency. There 
should also be an additional small term in the denominator to take into account 
the internal mechanical losses in the transducer element. With this type of ele- 
ment there are alarge number of possible variables with which to obtain optimum 
characteristics for the particular requirement. The mechanical Q can be adjusted 
by altering the effective mass or the acoustic loading. It is usually easier to 
adjust the acoustic loading by changing the radiating area of the head. 
In a projector, only the behavior in the neighborhood of resonance is usually 
important, and it is a simple matter using the foregoing equations to predict the 
lumped equivalent circuit when the electrostatic capacity is specified. Although 
the compound-bar transducer has been described in terms of a mass-loaded 
piezoelectric element, a very similar analysis canbe carried out for longitudinal 
mass-loaded magnetostriction units. 
Figure 1.6 is a photograph of four barium titanate mass-loaded compound 
elements ranging in resonant frequency from 120 kcpsto 5 kcps. The construction 
is similar in all cases: a barium titanate sandwich loaded with a head and a tail. 
Fig. 1.6. Typical transducer 
elements. 
