Impedance, acoustic mismatch

The use of air-bome ultrasound for the excitation and reception of surface or bulk waves introduces a number of problems. The acoustic impedance mismatch which exists at the transducer/air and the air/sample interfaces is the dominant factor to be overcome in this system. Typical values for these three media are about 35 MRayls for a piezo-ceramic (PZT) element and 45 MRayls for steel, compared with just 0.0004 MRayls for air. The transmission coefficient T for energy from a medium 1 into a medium 2 is given by... 

In view of the formidable technical difficulties, the results that have been achieved are all the more impressive. Figure 3.3(a) (see colour plate section) is an acoustic image of a bipolar transistor on a silicon integrated circuit taken at 4.2 GHz. There is a very severe acoustic impedance mismatch between helium and a material such as silicon. Even for normally incident waves 99 per cent of the power is reflected straight off the surface, and for waves incident at an angle greater than 3° all the power is reflected. For a lens of N.A. = 0.5,... 

When selective layers are deposited, the whole structure must be treated as a multiple resonator in which the reflection and/or refraction of the acoustic energy occurs at each interface. For example, when a polymer film is deposited on top of the gold electrode of the QCM, it is the polymer-Au interface with which we are concerned. When the mass loading of multiple structures becomes too high, the effect of the impedance mismatches becomes significant and the crystal ceases to oscillate. Even approximate treatment of the multiple resonator is difficult because densities, as well as thicknesses and shear moduli, of the individual layers must be known. 

The packaging (i.e., electrical insulation for operation in electrolytes) is more difficult with SAWs due to their rectangular geometry. SAWs are easier to fabricate with lithographic microfabrication techniques and therefore are more suitable for use in an array (Ricco et al., 1998). The choice of electrode materials is critical for QCM, where acoustic impedance mismatch can result in substantial lowering of the Q factor of the device. On the other hand, it does not play any role in the SAW devices. The energy losses to the condensed medium are higher in SAWs and this fact makes them even less suitable for operation in liquids. Nevertheless, SAW biosensors have been reported (Marx, 2003). 

Physical Modelling. The last method of synthesis, physical modeling, is the modeling of musical instruments by their simulating their acoustic models. One popular model is the acoustic transmission line (discussed by Smith in his chapter), where a non-linear source drives the transmission line model. Waves are propagated down the transmission line until discontinuities (represented by nodes of impedance mismatches) are found and reflected waves are introduced. The transmission lines can be implemented with lattice filters. 

With a sensitive pump-probe technique, possibly within a common-path interferometer, one can detect the acoustic vibrations of an individual gold nanoparticle [36]. This measurement directly gives the vibration s damping time, a parameter inaccessible to measurements on ensembles of nanoparticles, because of the inhomogeneity in sizes and shapes of populations of nanoparticles. The damping of vibrations of a nanoparticle depends critically on the acoustic impedance mismatch between particle and substrate materials, as well as on the mechanical contact area between them. Acoustic damping is therefore a probe of this contact, which may often be limited to a few nanometers only in diameter. 

If transmission measurements are impossible, another approach is to measure the amount of sound reflected at the interface between the sample and a known solid— often the container wall. The amount of sound reflected is a function of the impedance mismatch between sample and solid defined by a reflection coefficient, R 2. where z is the acoustic impedance of the material (= cp) (5). 

The bounding interface between the external and middle ear is the tympanic membrane. Pressure variations across the membrane move three ossicles, the malleus (hammer) connected to the membrane, the incus (anvil), and the stapes (stirrup) whose footplate is a piston-Hke structure fitting into the oval window, an opening to the fluid-filled cavities of the inner ear. Ligaments and muscles suspend the middle-ear ossicles so that they move freely. If sound reaches fluids of the inner ear directly, 99.9% of the energy is reflected [Wever and Lawrence, 1954], a 30-dB loss due to the mismatch in acoustic impedance between air and inner-ear fluids. Properties of the external meatus, middle-ear cavity, tympanic membrane, and middle-ear ossicles shape the responsiveness of a species to different frequencies. 

Solving Eq. 3 in the limit of small mismatches in acoustic impedance, hence negligible , shows the effect of the periodicity of the mirror. Considering the wavevectors for which q = m%ID, representing the boundaries of the Brillouin zone for a system with the periodieity of the Bragg mirror, more formally yields Eq. 2 for the frequencies at which bandgaps will be observed. 

Shown in Fig. 3.16 is a 1-3 piezoelectric composite with PZT ceramic rods embedded in a polymer resin. This structure is now widely used in medical ultrasonic transducers because the polymer helps reducing the acoustic impedance mismatch between human body and the PZT so that energy transmission becomes more efHcient. The load on the polymer phase can be transferred to the ceramic so that the effective load on the ceramic is enhanced, which produces higher electric signal when it is used as stress sensor. This composite structure also gives a much higher figure of merit for hydrophone applications [18],... 

One quantity which should be considered for mass correction is acoustic impedance mismatch which results from the difference in shear wave velocity and mass density between quartz and the deposited material. However, for the small mass loads discussed here this turned out to be of negligible importance. 

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