Frequency Equivalents

For energy to be absorbed, radiation of a frequency equivalent to E2-El must be supplied. Thus, using the Planck relation, the condition for absorption is defined as... 

The use of spur gears in gear pumps will produce in the discharge pulsations having a frequency equivalent to the number of teeth on both gears multiplied by the speed of rotation. The amplitude of these disturbances is a function of tooth design. The pulsations can be reduced markedly by the use of rotors with helical teeth. This in turn introduces end thrust, which can be eliminated by the use of doublehelical or herringbone teeth. 

Thus it is seen that m varies not only with vq, the frequency of the incident light, but also with the frequencies vq H- and Vq — v. The molecule will therefore emit radiation, not only with the frequency equivalent to the frequency of the absorbed radiation, but also with frequencies vq -j-and Vq — v. This elementary treatment of the Raman effect shows that the appearance of Raman lines is to be associated with a change of polarizability during oscillation. A more detailed treatment of the Raman effect involves the use of a more complex expression than 9.9 for the variation of a. 

P/VN and P-Np respectively. The onset temperature for P/ACE is in good agreement with that of the conventional value for Tg, consistent with the low frequency equivalence of the time-scale imposed by the phosphorescent label at this temperature in the PBA matrix. 

So, for two chemically distinct molecules or cliromophores A and B, with well-characterized vibronic excited states a and /S, a proximity-induced two-photon absorption process can be induced by tuning the exciting laser to a frequency equivalent to a mean of molecular excitation frequencies for the two molecules. 

First let us find the frequency equivalent of 1 eV from the Planck equation, and then find the wavelength from the frequency. 

The high-frequency equivalent circuit for a piezoelectric sensor is complex because of its mechanical resonance. This can be modeled by adding a series RLC circuit in parallel with the sensor capacitance and leakage resistance. The high-frequency equivalent circuit and its frequency response are shown in figure 2.3. In some applications, the mechanical resonance is desirable for accurate frequency control, as in the case of crystal filters. 

The two moduli are functions of temperature and frequency. The parameters G and tan 8, for a typical uncross-linked (unvulcanized) rubber or elastomer, are shown in Fig. 4.8 as a function of temperature (with frequency on the order of 1 Hz). The parameters are plotted against frequency, at a constant temperature, in Fig. 4.9. Thus, one observes that an increase in frequency (equivalent to an increase in strain rate) is similar to a decreased temperature. 

TOF turnover frequency = equivalents of secondary phosphine converted per equivalent of catalyst per unit of time. 

Ion dissociation was achieved by subsequent application of a voltage having a frequency equivalent to the secular frequency of the parent ion in the IT-SIMS. A typical voltage value was a few hundred millivolts. 

At higher frequencies, the leakage inductance begins to dominate the transformer s response. The high-frequency equivalent circuit is shown in Fig. 10.7, and transfer functions for voltage and current are given in Eq. (10.23) and Eq. (10.24). 

Here, m is the radial frequency (equivalent to 2 r/, where /is the frequency in Hertz) at time t, and AE is the amplitude in voltage. 

Rheological measurements on various vesicle phases have shown that the Cox-Merz rule - the complex viscosity of a sample at any frequency is equal to its apparent viscosity at the frequency-equivalent shear rate - is not fulfilled for these systems (10, 19-23) two examples of this are shown in Figure 10.25. At low frequencies or shear rates, respectively, both viscosities are equal, but beyond a certain shear rate the apparent viscosity is above the complex viscosity, and this difference increases with the shear rate. This behaviour can be qualitatively understood by a structural transition under the influence of shear. The oscillatory measurements do not lead to structural changes because in these experiments the deformation is normally kept below the limiting value for such a change. 

In case the performance of the CMS is limited by the occurrence of abnormality of the periodic signal causing difficulty to correcdy determine a point where the modulation drops to 10 %, an alternative method using a parallel bar chart shall be applied to verify the compliance of the CMS. In this case, a parallel chart containing black and white lines with a spatial frequency equivalent to the required resolution (MTF) shall be prepared and the distinguishability of the hne in the reproduced image on the CMS monitor shall be verified. 

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