. Biophysical science. Biophysics. 242 Mechanical Resonances of Biological Cells /13 : 4 modes of resonance, but it is impossible to determine the number of nodal diameters, much less examine the details of the shape necessary to distinguish various Figure 3. Photographs of rat red blood cells in ultrasonic fields. Note that there are some undistorted cells and some showing various modes of distortion. After L. Binstock and E. Ackerman. 4. More Exact Treatments In deriving the expressions for the resonant frequencies in Sections 2 and 3, a number of assumptions were made. The validity
. Biophysical science. Biophysics. 242 Mechanical Resonances of Biological Cells /13 : 4 modes of resonance, but it is impossible to determine the number of nodal diameters, much less examine the details of the shape necessary to distinguish various Figure 3. Photographs of rat red blood cells in ultrasonic fields. Note that there are some undistorted cells and some showing various modes of distortion. After L. Binstock and E. Ackerman. 4. More Exact Treatments In deriving the expressions for the resonant frequencies in Sections 2 and 3, a number of assumptions were made. The validity of these is considered in more detail in this section. To a physicist, probably the most noticeable assumption was the absence of viscosity in the fluids. Readers with more biological training would emphasize the nonspherical shape of all real cells. Other factors, explicitly or implicitly neglected, include the effects of the compressibility of the liquids, the relationship of breakdown rate to resonance, and the actual modes present. The major effect of viscosity is to damp any free vibration. With the geometries chosen in this chapter and typical viscosities measured for protoplasm, that is, coefficients of viscosity from 2 to 10 centipoise, this damping is very pronounced. The net result is to broaden the resonance curve as shown in Figure 4; the curve including viscosity has a mechani- cal Q of the order of Nonetheless, the resonant frequencies are only 1 The quality factor Q of a resonance may be defined in several equivalent forms. For the purpose of this chapter, it may be considered to be defined by the relationship Q =/o/A/ where A/ is the width of the band between the two frequencies at which the square of the amplitude of the response of a vibrator is decreased by a factor of two from its value at the resonant frequency f0 provided the vibrator is driven by a force of constant amplitude. The greater the damping, the broader will be the resonance and the lower th
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