By D. S. Ballantine Jr., Robert M. White, S. J. Martin, Antonio J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Moises Levy, Richard Stern
Written via an interdisciplinary team of specialists from either and academia, this publication presents an in-depth examine the present nation of acoustic wave units and the scope in their use in chemical, biochemical, and actual measurements, in addition to in engineering functions. as a result of the inherent interdisciplinary purposes of those units, this publication may be invaluable for the chemist and biochemist drawn to the use and improvement of those sensors for particular purposes; engineer fascinated about the layout and development of those units; the chemical engineer and the biotechnologist attracted to utilizing those units for strategy tracking and regulate; and the sensor neighborhood at huge.
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Additional info for Acoustic Wave Sensors - Theory, Design, and Physico-Chemical Applications
Also, propaga4The quantity with physical significance is understood to be the real part of the expression for ui. The exponential can be written in terms of sine and co- sine functions using Euler's identity, e -~x= cos(x) + jsin(x), from which the displacement is seen to be u,(x,t) = uiocos(o~'- kx). A similar approach is used by electrical engineers to represent sinusoidally varying currents and voltages. ~The phase velocity is the speed at which one must travel to keep the phase of a sinusoidal wave at a constant value.
The waves are generated only at the electrodes because those are the only regions in the crystal where the piezoelectric source term eiytE varies spatially. 1) where A and B are constants, ta is the angular excitation frequency (to = 2"trf), k is the wavenumber, t is time, and j = ( - 1 ) 1/2. 3, which may be thought to originate at the top electrode. After transiting the crystal, this wave is reflected (with phase shift due to reflection ~br = ~r) at the bottom crystal face, returns to the top electrode where it again reflects (with ~b,.
11), the presence of an additional term involving the electrical potential ~b is apparent. This term may be considered as a source term responsible for the generation of an acoustic wave by an applied, time-varying electrical potential, s Conversely, the wave displacements generate an accompanying electrical potential through which the piezoelectric wave can be electrically detected. 28 represents three equations in four unknowns: ul, u2, u3, and ~b. 26 by noting that in a region with no free charges, the electrical displacement is solenoidal (V • D = 0).
Acoustic Wave Sensors - Theory, Design, and Physico-Chemical Applications by D. S. Ballantine Jr., Robert M. White, S. J. Martin, Antonio J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Moises Levy, Richard Stern