Reflection Coefficient - The Corresponding Frequency Spectrum - Engineering Assignment Help

Assignment Task :

Task

This assignment consists of the following 10 (ten) questions relating to Topics 1 and 2, which should be answered providing all relevant explanations and calculations. Ensure you include all units in your workings and final answer.

Rationale

This compulsory assignment is designed to promote student insight and research into various aspects of Topics 1&2.

The assignment will promote the following learning outcomes, in particular:

• the ability to describe and solve numerical problems pertaining to the physical properties of diagnostic ultrasound and to its interaction with body tissue,

• the ability to explain the design and operation of diagnostic ultrasound transducers,

• the ability to quantify characteristics of the ultrasound beam relating to it its spatial extent and frequency content.

Question 1

1. From the figure below, calculate the wave amplitude, period and frequency. Each major division along the (vertical) y-axis is 1 volt and each major division along the (horizontal) x-axis is 100 nanoseconds. What is the wave propagation speed c if the wavelength λ of this wave is 3.58 x 10-4 m?

Question 2

a) For a 5.00 MHz ultrasound beam of intensity 25.0 mW cm - 2 traveling in fat, calculate:

i. The density of the fat.
ii. The particle displacement amplitude.
iii. The particle velocity amplitude.
iv. The acoustic pressure amplitude.
 

b) For the three different amplitude values you have found above, briefly state how these values compare, and discuss whether this is what you would expect.
 

Question 3
a) An ultrasound pulse suffers a -35 dB change when passing through a 30 cm thickness of soft tissue. Find the following values if the original transmitted intensity into the
tissue was 50 mWcm -2.
i. The final intensity.
ii. The ratio of the final pulse amplitude to the initial pulse amplitude.
 

b) An ultrasound pulse traveling in fat has normal incidence upon a layer of muscle.
i. Calculate the reflection and transmission coefficients
ii. Express the reflective loss in deciBels
 

Question 4
a) An ultrasound beam traveling in soft tissue is incident upon a layer of fat, striking the boundary at an angle of 65 o to the boundary. Calculate the change in direction
between the incident beam and the transmitted beam.
b) Explain what is meant by the term Critical Angle, and provide clear specifications of the critical angle for a soft tissue / fat interface.
 

Question 5
A 4 MHz transducer with a PZT - 4 piezo-electric crystal has a matching layer of a material with an acoustic impedance of 1.84 x 10 6 Kg m -2 s -1 and density of 1150 Kg m -3.
a. Calculate the proportion of ultrasound that passes from the transducer into the soft tissue if the matching layer thickness is 0.005 mm.
b. Calculate the proportion of ultrasound that passes from the transducer into the soft tissue if the matching layer thickness is 0.072 mm.
c. Design an ideal matching layer for an 8 MHz transducer with a PZT - 5 piezo-electric crystal.
 

Question 6
A 5 MHz sound wave of intensity 40 mW cm -2 travels a distance of 5 cm to an interface between soft tissue and muscle, where it is partially reflected, directing the reflected pulse
back through the 5cm of tissue to the point where it started.
a. Calculate the reflection coefficient for the interface.
b. Estimate the difference between the initial and final intensities in decibels.
c. Calculate the ratio of the final amplitude of the sound wave to its initial amplitude.
 

Question 7
The amplitude time characteristics for a pulse of ultrasound are as shown in the diagram. Sketch the corresponding frequency spectrum.

Question 8  

A 7.5 MHz transducer is constructed with a crystal of diameter 8.0 mm and has a curved surface to focus the beam at a depth of  35 mm. Make the necessary calculations to complete the following:-  

1. Draw the effective beam profile for the focussed transducer, also showing the theoretical and effective beam profiles for the corresponding plane transducer for comparison.

2. Sketch a graph of the central axis intensity along the beam, indicating the estimated positions of maxima and minima.

3. Classify the focusing capability of the transducer.

4. Define the term "focal zone" and estimate its dimensions for this transducer.

Question 9  

1. Write brief notes to explain the piezo-electric effect and its role in generating a pulse of ultrasound.

2. Explain the use of time delays to steer and focus the ultrasound beam in a phased array sector scanning transducer.

Question 10  

A 3.5 MHz phased array transducer consists of twenty 1 mm wide piezoelectric elements with a 0.1 mm gap between each element. Delay lines are used to both focus and steer the ultrasound beam in soft tissue. The elements are each 15 mm long and are mechanically focussed in the elevation direction.

1. Sketch the lateral beam profile if all elements are pulsed simultaneously. 

2. Find the value of the effective near field length if all elements are pulsed simultaneously. 

3. Calculate the time delay between firing the central and outer elements, if the effective radius of curvature of the ultrasound wavefront is 80 mm, and the beam is directed along the transducer axis or “un-steered”.

4. Calculate the time delay between the two end elements if the beam is steered 20°away from the transducer axis or ‘un-steered’ direction and unfocused.

5. Calculate the time delay between each end element and the central element if the beam is steered 10o away from the transducer axis and the focal depth is 55 mm, as measured along the axis of the transducer.

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