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

3.3 Ultrasonic techniques

pT : amplitude of the sound pressure at the transducer; pR : amplitude of the sound pressure at the receiver; X : transducer spacing; r : reflection coefficient; β = 2π/λ : wave number; γ = α+iβ : complex propagation constance.

The cosine function of the transfer function Eq.(3.62) describes the so-called λ/2-ripple, caused by the multiple reflections of the signal at the transducers. For αλ > 3 the denomi- nator of Eq.(3.62) equals approximately 1, so that an exponential decay of the sound wave pR ∼e−αX follows. In Fig.(3.11) a plot of Eq.(3.62) is given as an example. It illustrates that at decreasing sample length X the standing wave contributions of the ultrasonic field within the cell become more and more important.

Figure 3.11: Effects of the cosine term in Eq.(3.62) on the transfer function.

Fitting at a given frequency f Eq.(3.62) to experimental data yields the absorption coef- ficient α and the sound velocity cs = λf of the sample liquid. To raise the accuracy of α measurements it is usual to reduce the influence of the cosine function. This can be realized with the help of the pulse modulation as mentioned before. The transducer signal is pulsed with the aid of square-wave pulse, with the pulse length following the relation:

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