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3.3 Ultrasonic techniques

The real resonator

• Quality factor the real resonator In a real resonator, however, acoustic energy is not only dissipated by the liquid sample but also by imperfections of the cell. Among the various mechanisms is energy dissipation caused by diffraction of the sound wave due to the finite cell di- ameter. Furthermore, the radiative energy losses at the back face of the quartz, have also to be taken into account. The quality factor Q of a resonator is defined, by the ratio of reversibly stored energy Er and the dissipative energy Ed: Q ≡2πEr/Ed. In summary, there are two contributions to the energy dissipation of a sound beam: attenuation caused by the liquid and that from the instruments. The total measured reciprocal quality factor can be written as:

Because the quality factor Q is connected with the half-power bandwidth ∆f via: Q = fn/∆f and because of Eq.(3.50) the total attenuation per wavelength, can be expressed by:

Labhardt et al. [61], [62] have found a relation for losses of plane transducer res- onators:

where βb = ZL/ZT, with the specific impedances of liquid ZL and transducer ZT. The second term on the right-hand side of Eq.(3.52) describes losses caused by diffraction of the sound beam, while Vr additional losses. However, it is not pos- sible to analytically separate all instrumental loss contributions during measure- ments. Owing to this, it is necessary to perform a reference measurement, with a carefully chosen reference liquid with matched sound velocity and density, and to use Eq.(3.50) to calculate Qliquid.

• Transducer properties: The resonances of the transducer can be expressed by the sound velocity of the

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