Re: transducer - adjusting of tightness You probably are thinking of impedance matching networks sometimes put between the transducer and the pulser. Their purpose is to match the impedance of the pulser to that of the transducer which will produce maximum energy transfer between them. The impedance of the amplifier is usually neglected because during the pulse the protective diodes are very low impedance. I do not have many references in my library but the basic principles of impedance are usually covered in basic electronics textbooks.
I have an old book by Warren P. Mason 'Physical Acoustics and the Properties of Solids' with the a section on this subject. Section 3.3 titled 'Equivalent Circuits of Piezoelectric Crystals and Their Applications to Obtaining Maximum Energy Transfer.' Although this book was published in 1958 this is a solid exposition on this subject.
To quote this text 'By adding electrical or mechanical elements it is often possible to make the circuits into the form of filter sections which can be designed to match the electrical and mechanical conditions at the driving and receiving end.' This approach is not popular in NDT because in general it is difficult to obtain broadband filters without the use of active components. I know of one or two manufacturers who have at least experimented with active filters but they have not caught on in the market.
You can do a search of JASA and similar journals and find some more articles on this subject. The ultrasonic cleaning, impact grinding, sonoluminescence, and sonochemistry fields do use such matching networks. So you might look for articles in those areas as well.
Or maybe I have misinterpreted what you are looking for?
: Can somebody help me with where to find a how-to for adjusting the transducer voltage with a capacitor.