# Daily Archives: March 9, 2021

## Calculate the series and parallel resonant frequencies of the crystal.

A piezoelectric crystal has an effective mass of 10−2 kg, stiffness of 1010 N m−1 and damping constant 200 Ns m−1 . The electrical capacitance of the crystal is 1000 pF and the charge sensitivity is 2 × 10−10 C N−1 .

(a) Calculate the series and parallel resonant frequencies of the crystal.

(b) Calculate the magnitude and phase of the overall electrical impedance of the crystal at the above frequencies.

(c) The crystal is incorporated into a closed-loop oscillator system which is to oscillate at the crystal series resonant frequency. Calculate the required gain and phase of the maintaining amplifier at this frequency.

## Calculate the ‘round trip’ time TT and the fraction of received power to transmitted power.

An open steel vessel contains liquid metal to a depth of about 0.75 m. It is proposed to measure the depth of liquid using ultrasonic pulse reflection techniques. A quartz crystal attached to the base of the vessel is to act alternatively as a transmitter and receiver. Using the data given below and in

(a) Calculate the ‘round trip’ time TT and the fraction of received power to transmitted power.

(b) Choose suitable values for pulse width and repetition times.

Data

Velocity of sound in liquid metal = 1.5 × 103 m s−1

Density of liquid metal = 5 × 103 kg m−3

Power attenuation coefficient = 0.1 m−1

Natural frequency of quartz crystal = 1 MHz

## Find the difference between the frequencies of the transmitted and received beams when the flow rate is 1.13 × 103 m3 h−1.

An ultrasonic Doppler flowmeter is to be used to measure the volume flow rate of a slurry in a steel pipe of diameter 0.2 m. Two piezoelectric crystals, each having a natural frequency of 1 MHz, are positioned, a few millimetres apart, on the outside of the pipe to form an ultrasonic transmission link. The transmitting crystal directs an ultrasonic beam into the pipe so that the beam is moving in an opposite direction to the flowstream. The angle between the ultrasonic beam and the direction of flow is 60°. On average 10% of the ultrasonic power reaching each solid particle is scattered back in the direction of the receiving crystal. Assume that the slurry has the same density and sound velocity as water and a power attenuation….

## Explain in detail what modifications should be made to the transducer so that the signal entering the tissue is a close approximation to a single pulse.

An ultrasonic transmitter is in the form of a piezoelectric disc of diameter 2.5 cm and thickness 1.0 cm. The front face of the disc is placed directly onto biological tissue; the rear face is in contact with air. A pulse launched from the centre of the disc divides into two equal pulses, each of power 1 W and width 0.5 µs, one travelling towards the front face and one towards the rear face.

(a) Use the data given below to derive the form of the signal entering the tissue.

(b) Explain in detail what modifications should be made to the transducer so that the signal entering the tissue is a close approximation to a single pulse.

## Explain briefly the meaning of the following terms used in ultrasonics:

The overall transmission coefficient αT,G between a transmitter of characteristic impedance R1 and a gas of impedance R2 separated by a matching layer of impedance R is given by eqn [16.40]. By differentiating [16.40] and setting the derivative equal to zero (or any other method), show that αT,G is a maximum when

(a) Explain briefly the meaning of the following terms used in ultrasonics:

(i) Attenuation

(ii) Matching layer

(iii) Resonant stationary wave.

(b) An ultrasonic transmitter is in the form of a piezoelectric disc of diameter 1.0 cm and thickness 2.0 mm. The transmitter is to be used to launch 1 MHz pulses into biological tissue. Use the concepts of part

(a) and the data below to detail what modifications are made to the transmitter so it meets the following specification:

….

## Find the bit rate and minimum transmission bandwidth for the PCM sign

A sample containing oxygen and nitrogen is injected into a helium carrier at time t = 0. The sample is swept through a column 1.0 m long packed with molecular sieve. The eluting components are detected by a katharometer detector which has an equal sensitivity for oxygen and nitrogen. The time variation in katharometer output voltage is shown in Figure Prob. 1.

(a) Assuming that the distribution ratio K for oxygen is 2.0, estimate the mean carrier velocity ó and K for nitrogen.

(b) Estimate base width ∆t for both peaks and hence find the resolution R.

(c) Estimate the number of theoretical plates N and HETP.

(d) Estimate the percentage composition of the sample (assume peaks are approximately triangular).

1. Sixteen analogue input voltages,….

## Explain briefly the meaning of the following terms used in ultrasonics:

The overall transmission coefficient αT,G between a transmitter of characteristic impedance R1 and a gas of impedance R2 separated by a matching layer of impedance R is given by eqn [16.40]. By differentiating [16.40] and setting the derivative equal to zero (or any other method), show that αT,G is a maximum when

(a) Explain briefly the meaning of the following terms used in ultrasonics:

(i) Attenuation

(ii) Matching layer

(iii) Resonant stationary wave.

(b) An ultrasonic transmitter is in the form of a piezoelectric disc of diameter 1.0 cm and thickness 2.0 mm. The transmitter is to be used to launch 1 MHz pulses into biological tissue. Use the concepts of part

(a) and the data below to detail what modifications are made to the transmitter so it meets the following specification:

….

## Calculate p(0) such that p(y) is normalised.

A PCM transmitter sends out a 12-bit serial digital signal with 5 V corresponding to a 1 and 0 V corresponding to a 0. The signal passes over a transmission link, affected by random noise, to a PCM receiver consisting of a low-pass filter and a comparator. The comparator input signal is the PCM signal with noise superimposed on it; the probability density p(y) of this noise is the triangular function shown in Figure Prob. 2. The comparator decides that a 1 has been transmitted if the comparator input signal is greater than 2.5 V, and that a 0 has been transmitted if the comparator input signal is less than or equal to 2.5 V.

(a) Calculate p(0) such that p(y) is normalised.

(b) Find are probability that….

## estimate the probable number of errors if 1600 bits of information are transmitted.

Ten measurement signals are input to a multiplexer so that each one is sampled twice per second. The multiplexed signal is input to a serial digital transmitter incorporating a 10-bit ADC. The resulting PCM signal is converted into FSK such that 720 Hz corresponds to a 1 and 480 Hz corresponds to a 0. Estimate the bandwidth required by the FSK signal.

(a) Random noise is characterised by a Gaussian probability density function of standard deviation  V and mean value  Using the probability values given below, calculate the probability that the noise voltage:

(i) exceeds +0.5 V

(ii) lies between −1.0 and +1.0 V

(iii) is less than −1.5 V.

(b) Information in binary form is sent with a 0 represented by 0 V and a 1 represented by 5….

## Calculate the cost per equivalent unit of material and conversion cost for January

Calculate the cost per equivalent unit of material and conversion cost for January – using the Weighted Average Approach Units Materials Conversion Work in process January 1 2,500 50% 35% Work in process January 31 45% 25% Materials cost in work in process January 1 \$25,000 Conversion costs in work in process January 1 \$10,000 Units started in production 12,000 Units transferred to the next department 8,000 Materials cost added during January \$20,000 Conversion costs added during January \$7,500 Complete the grey cells that required information. Beginning Inventory Units Started this Period Units to be accounted for Direct Materials Conversion Costs Units in process January Units completed & transferred out Ending Inventory Units accounted for Direct Materials Conversion Costs Beginning Inventory Current Costs Total Costs Equivalent Units Materials….