Doppler frequency, variation with

Figure 3. Variation in Doppler frequency with orientation angle of the membrane system. Doppler frequency and ion velocity increase as the motion becomes more perpendicular to the optical axis.

In principle, the ultrasonic techniques described for solid-liquid flow measurement can be applied to measure air flow rate and particle velocity. Direct measurement of air flow rate by measuring upstream and downstream transit times has been demonstrated. But, the Doppler and cross-correlation techniques have never been applied to solid/gas flow because the attenuation of ultrasound in the air is high. Recent developments have shown that high-frequency (0.5-MHz) air-coupled transducers can be built and 0.5-MI Iz ultrasound can be transmitted through air for a distance of at least 1 in. Thus, the cross-correlation technique should be applicable to monitoring of solid/gas flow. Here, we present a new cross-correlation technique that does not require transmission of ultrasonic waves through the solid/gas flow. The new technique detects chiefly the noise that interacts with the acoustic field established within the pipe wall. Because noise may be related to particle concentration, as we discussed earlier, the noise-modulated sound field in the pipe wall may contain flow information that is related to the variation in particle concentration. Therefore, crosscorrelation of the noise modulation may yield a velocity-dependent correlation function. 

The Doppler shift of frequency due to motion of the wave source relative to the point of observation can be an explanation of the phenomenon observed. A theoretical prediction of wave emission from the tip of a crack penetrating through ice floe was made by Slepyan (1993). The asymptotic solution presumes the emission of shear bending waves with frequency of about 0.58 Hz, wave length 38.5 m and phase velocity equal to 22.4 m/s for the crack moving faster than Kelvin s phase velocity. Smirnov and Shushlebin (1988) observed variations in frequency of seismic waves related, they assume, to movement of the crack tip. 

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