Acoustical phase shift

The high mass sensitivity calculated in the previous example justifies the term microbalance in describing the sensing capabilities of the quartz resonator. Equation 3.9 can be used to calculate fr uency shifts for surface accumulations that behave as ideal mass layers. A real film behaves as an ideal mass layer if it is sufficiently thin and rigid so that it moves synchronously with the oscillating device surface. On a TSM resonator, this condition is realized if the acoustic phase shift across the film is small, i.e., ir. The phase shift is... 

An ideal mass layer is assumed to have an infinitesimal thickness, yet contribute a finite areal mass density to the device surface. In Section 3.1.1, we noted that this criterion holds as long as the acoustic phase shift across the film is small compared with ir. The equivalent-circuit model for the mass-loaded resonator can be determined from the surface mechanical impedance contributed by a surface perturbation. The surface stress required to sinusoidally accelerate a mass layer is [14]... 

The dynamic behavior of the film s shear displacement vs position across the film thickness hf can be predicted from a continuum electromechanical model described by Reed et al. [10]. Several distinct regimes of dynamic behavior can be identified [40], determined by the acoustic phase shift, , across the film. 

Figure 3.15 The dynamic film response generated by the oscillating resonator surface varies with the acoustic phase shift across the film [40] (a) for vfl, synchronous motion occurs (b) for s itfl, overshoot of the upper film surface in-plu with the resonator surface occurs (film resonance occurs when = a/2) (c) for > irfl, the upper film surface is 180° out-of- diase. The film is the thin region at the top the crystal is below. (Repraaed widi permission. See Ref. [40]. 1991 IEEE.)...

Acoustic phase shift in quartz crystal fcth Root of Bessel function of order m Element of permittivity tensor... 

In Sect. 2.7.2.1.2, the phenomenon of film resonance was discussed. In this special situation, the film thickness corresponds to one quarter of the acoustic wavelength, that is, the acoustic phase shift defined by Eq. (11) has the numerical value = 7t/2. For a film of given shear modulus, progressive increase in thickness will eventually result in this condition being satisfied. This phenomenon is illustrated in Fig. 27 [41] for a poly(3-hexylthiophene) film as a function of the polymerization charge during deposition. As can be seen, the resonant frequency transiently moves sharply upwards and the peak amplitude... 

Here, 0E is the phase shift introduced by the compensating (stretched) line, lr and ls are the length of the reference and of the sensing channel, respectively, and vr and vs are the acoustic velocities in the two channels. The output of the sensor (Vo) is then... 

The results presented demonstrate that auditory systems of animals and humans respond to pulsed microwaves. However, there is little likelihood of the microwave acoustic effect arising from direct interaction of microwave pulses with the cochlear nerve or neurons at higher structures along the auditory pathway. The pulsed microwave energy, instead, initiates a thermoelastic wave of pressure in the head that travels to the cochlea and activates the hair cells in the inner ear. This theory covers many experimental observations, but it may be incomplete and thus require further extension to account for certain additional experimental findings. Tyazhelov, et al. (1 1) found in their beat frequency experiment that matching of microwave pulses (10 ps, 8000 pps) to a phase-shifted 8 kHz sinusoidal sound input... 

Moreover, in recent years broad band lasers have appeared which lack any frequency modal structure, at the same time retaining such common properties of lasers as directivity and spatial coherence of the light beam at sufficiently high spectral power density. The advantages of such a laser consist of fairly well defined statistical properties and a low noise level. In particular, the authors of [245] report on a tunable modeless direct current laser with a generation contour width of 12 GHz, and with a spectral power density of 50 /xW/MHz. The constructive interference which produces mode structure in a Fabry-Perot-type resonator is eliminated by phase shift, introduced by an acoustic modulator inserted into the resonator. 

The oscillating resonator surface may be considered as a source for shear waves that are radiated into the contacting film. The upper film surface reflects these radiated shear waves downward, so that the mechanical impedance seen at the quartz surface is dependent upon the phase shift and attenuation undergone by the wave in propagating across the film. When the film is rubbery, significant phase shift across the film occurs. Consequently, the coupling of acoustic energy into the film depends upon thin-fllm interference. 

Even though these transitions are different in many ways, as demonstrated below, the way in which acoustic energy interacts with polymeric materials permits us to use AW devices to probe changes in polymer film viscoelastic properties associated with these transitions. It should be emphasized up front, however, that evaluating the viscoelastic properties (e.g., modulus values) requires an ability to effectively model the film displacement profiles in the viscoelastic layer. As described in Section 3.1.8, the film displacement effects are dictated by the phase shift, , across the film. Since depends on film thickness, perturbations in acoustic wave properties due to changes in viscoelastic properties (e.g., during polymer transitions) do not typically depend simply on the intrinsic polymer properties. This can lead to erroneous predictions if the film... 

Let us assume that the crystal has been coated with a thin film of thickness df. Let the film have the same acoustic properties as the crystal, hi this case, the entire acoustic wave enters the sample. Evaluating rq,2 as the ratio Mq(zq,2)/Wq(zq,2). we find the modulus rq,2l as unity. There is a phase shift Aq) =- 2kfd which the wave acquires while traveling through the film. We find ... 

FIGURE 4.7 SAW velocity and attenuation changes vs. shear wave phase shift (i) for several values of film loss parameter. The dashed line corresponds to prediction using Tiersten formula. (Reprinted with permission from Martin S. J., Frye G. C., and Senturia S. D., Dynamics and response of polymer-coated surface acoustic wave devices Effect of viscoelastic properties and film resonance, Anal. Chem., 66, 2201-2219, 1994. Copyright (1994) American Chemical Society.)... 

Yoo BK, Park YW, Kang CY, Yoon SJ, Kim JS et al. (2006) Surface acoustic wave sensors to detect volatile gases by measuring output phase shift. J. Electrocer. 17 1013-1017. 

The PEM is made of a piezoelectric transducer that is glued to a ZnSe crystal. The piezoelement converts a periodic voltage to a periodic mechanical (acoustic) wave, which compresses or expands the crystal. This movement changes the refractive index in the x direction and imposes a periodic retardation (or acceleration) of the fix component of the incident linearly polarized wave. The fiy component remains unchanged. The PEM is operated at its resonant frequency (50 kHz). If the optical element is at rest, the polarization of the radiation remains unchanged. If the optical element undergoes compression or expansion, the component fix has a positive (retardation) or negative (acceleration) phase shift relative to the phase component of the component fiy. 

There is an additional phenomenon worthy of mention for viscoelastic films - film resonance. As film thickness increases, an acoustic phase delay () develops across the film. One can show[l, 24] that the phase shift developed across a film of thickness hf and shear modulus G is given by... 

Fast motions of a bubble surface produce sound waves. Small (but non-zero) compressibility of the liquid is responsible for a finite velocity of acoustic signals propagation and leads to appearance of additional kind of the energy losses, called acoustic dissipation. When the bubble oscillates in a sound field, the acoustic losses entail an additional phase shift between the pressure in the incident wave and the interface motion. Since the bubbles are much more compressible than the surrounding liquid, the monopole sound scattering makes a major contribution to acoustic dissipation. The action of an incident wave on a bubble may be considered as spherically-symmetric for sound wavelengths in the liquid lr >Ro-When the spherical bubble with radius is at rest in the liquid at ambient pressure, pg), the internal pressure, p, differs from p by the value of capillary pressure, that is... 

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