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Original English dissertation · scientific equations reproduced directly from the source PDF.

3.3 Ultrasonic techniques

Figure 3.7: Basic principle of an ultrasonic cell.

receiver3as a mathematical series:

Original equation (3.41) from dissertation page 41
Equation (3.41) · original 2007 dissertation

This series convergences for rR ·rT < 1. With pT(0,t) = p0 ·eiωt this yields:

Original equation (3.42) from dissertation page 41
Equation (3.42) · original 2007 dissertation

Finally, the transfer function T(f) results as proportionality:

Original equation (3.43) from dissertation page 41
Equation (3.43) · original 2007 dissertation

Its absolute value is:

Original equation (3.44) from dissertation page 41
Equation (3.44) · original 2007 dissertation

with:

3index R denotes the receiver and index T the transducer

View original page 41 (authoritative equations, figures and layout)Original dissertation PDF page 41

Original dissertation · PDF page 41 · reader page 33 of 132

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