1. A piezoelectric crystal has an effective mas of 5X10-2 kg, stiffness of 2)(1010 N/m and a damping constant 200 Ns/m. The electrical capacitance of the crystal is 1600pF and the charge sensitivity is 2X10-10 C/N.
i) Calculate the series and parallel resonant frequencies of the crystal.
ii) The magnitude and phase of the overall electrical impedance of the crystal at the above frequencies.
2. With an aid of a block diagram, derive the equation of the frequency shift and the adder output signal equation for an ultrasonic Doppler flow meter.