Beat frequency/pattern

An interesting modification of this technique is the fibre-optic dynamic anemometer (FODA)143. A length of fibre-optic cable carries the laser beam to the interior of the dispersion. Back-scattered light, with its Doppler frequency shift, is returned to the detector along with reflected light and, again, the resulting beat frequency pattern is analysed. Since only a very small volume around... 

The observed noise spectrum of a fluorescence signal excited by a laser with flie beat frequency pattern of Eq. 52 is then the product of (52) and (50), or... 

The case spectra made of superposition of cycles is the most frequent in real life and can be analyzed by the Fourier transform, as seen in Sect. 8.5. Some key examples from the simplest to the most complex superposition are offered in Fig. 8.43. The time history (a) of Fig. 8.43 is the simplest case made of two sine waves of slightiy different amplitude and closely-spaced frequencies. Combined the two waves show the characteristic beat frequency pattern. It is a narrow-band process because in the time period T it can be counted 5 zero upcrossing and 5 peaks with an irregularity factor y — 1, see Eq. (8.2). Case (b) of Fig. 8.43 refers to a high frequency load cycle of amplitude Sai and angular frequency coif superimposed to a low frequency cycle of amplitude Sa2 and angular frequency u>2t, with < Sa2 and CO2 [Pg.454]

Fig. 8.43 a Time history of a narrow-band beat frequency pattern, b High frequency-low amplitude cycles superimposed to low frequency-high amplitude base line cycle, c High frequency- high amplitude cycles superimposed to low frequency- low amplitude base line cycle, d Random time history... 

Nonciliated cells separate fields of ciliated epithelial cells from each other. Synchronized ciliary movement, with a beat frequency in human proximal airways under normal conditions of 8-15 EIz, propels mucus along the mucociliary escalator at a rate of up to 25 mm/min. Beat frequencies appear to slow to roughly 7 Hz in more distal airways. Cilia move in the same direction and in phase within each field but cilia in adjacent fields move in slightly different directions and are phase shifted. These beat patterns result in metachronal waves that steadily move mucus at higher velocities ( -12-18 mm/min) than would be achievable by summing the motion of individual cilia. 

Chilvers, M. A. and O Callaghan, C., Analysis of ciliary beat pattern and beat frequency using digital high speed imaging comparison with the photomultiplier and photodiode methods, Thorax, 55, 314-317, 2000. 

Mixing this broadened, scattered signal with incident light produces a pattern of beat frequencies, the measurement of which allows the diffusion coefficient of the particles to be calculated. 

Figure 6.5 Entanglement between electron and nuclear spins, demonstrated by Mehring and co-workers in 2003. The time dependent signal is an interferogram which exhibit two patterns of oscillations, one with phase 01+02 and the other 0i —02, where 0i 2 are rotation angles about the z-axis. On the right the Fourier transform of the signals showing the two beating frequencies. Adapted with permission from [19].

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

Figure 4.2b is a presentation of the FID of the decoupled 13C NMR spectrum of cholesterol. Figure 4.2c is an expanded, small section of the FID from Figure 4.2b. The complex FID is the result of a number of overlapping sine-waves and interfering (beat) patterns. A series of repetitive pulses, signal acquisitions, and relaxation delays builds the signal. Fourier transform by the computer converts the accumulated FID (a time domain spectrum) to the decoupled, frequency-domain spectrum of cholesterol (at 150.9 MHz in CDC13). See Figure 4.1b.

Figure 12.1. Beat pattern resulting from interference between two similar frequencies.

When the nuclei are subjected to an electrical quadrupole interaction, the NFS pattern shows quantum beats with a single frequency corresponding to the energy difference between the sub-levels of the exited state (AEq), which is equal to the... 

Figure 6. ISRS data from a-perylene crystal at two temperatures, recorded with transient grating experimental arrangement. Oscillations in each sweep due to 80- and 104-cm optic phonons. Data contain sum and difference frequencies that produce beating pattern.

This expression describes the important case of an inhomogeneously broadened band with homogeneously broadened components. If the number of components is small or they are regularly spaced in frequency, a beat pattern for C(t) is obtained. Exjjerimentally, a time-resolved CARS experiment (which gives C(t) for t > tp) displays directly this oscillatory behavior, as was observed in an early study of (Fig. 5). The corresponding Raman... 

Other excitation energies Other than the ones at S, + 1380 and S, + 1420 cm-, there are three prominent bands in the intermediate region of jet-cooled anthracene s excitation spectrum. Time- and frequency-resolved measurements subsequent to excitation of these bands have also been made. Without going into any detail concerning the results of these measurements, we do note that all three excitations give rise to quantum beat-modulated decays whose beat patterns (phases and modulation depths) depend on the fluorescence band detected.42 Figure 16 shows an example of this behavior for excitation to S, + 1514 cm-1. The two decays in the figure correspond to the detection of two different fluorescence bands in the S, + 1514 cm-1 fluorescence spectrum. 

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