Final Ultrasound Report PDF

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Final report of the last three weeks of experiments...

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Difference in Acoustic Impedance throughout Household Materials

Abstract: Acoustic impedance is a measure of how easily a sound wave travels through a certain medium, how much of it is absorbed and/or reflected. Ultrasounds utilise the difference in acoustic impedance of materials such as tissue, bone and organs to decipher and form an image of the human body through ultrasonic waves. The experiment aims to compare the difference in acoustic impedance of household materials. It was found foam had the lowest acoustic impedance, absorbing the most amount of sound and the notebook had the highest, as it reflected the most amount of sound. Regardless of the many variables, adequate results were found and allowed a visualisation of how the acoustic impedance varies during an ultrasound, allowing for accurate images to be formed.

Introduction Acoustic impedance (Z) is the product of its density and the acoustic velocity (NDT Education Resource Centre). In simplistic terms, acoustic impedance of a medium is a measure of how easy it is to transmit sound waves through the certain medium. The smaller the acoustic impedance of a material is, the more the sound will be absorbed and the less will be reflected. The larger the acoustic impedance of a material, the more resistant it will be to the transmission of sound through it, resulting in more of the sound being absorbed and less of it being reflected (Warren, N., 2011). Therefore, the acoustic impedance is dependent on the speed of a wave through the certain material and the density of that material, resulting in the acoustic impedance varying for each type of material. This can be utilised when using ultrasound and ultrasonic waves. Ultrasound is acoustic energy in the form of waves which have a frequency above hearing range (Rouse, M.). The highest audible frequency for humans is 20, 000 Hz or 20 kHz, with the ultrasound range starting at this frequency. Ultrasound is utilised for a wide variety of modern uses, such as: electronic, navigational, security and medical. Ultrasound technology was first implemented in World War I as underwater transducers. Water has a high acoustic impedance meaning much of the ultrasonic waves are absorbed, leading to it being able to travel long distances and be highly sensitive. This is further Page 1 of 8

illustrated throughout the animal kingdom, as intelligent underwater lifeforms (i.e. whales and dolphins) use ultrasonic waves to find certain objects, identify targets and communicate with one another (David, J., Cheek N, 2012). The fact that ultrasound waves travel with a higher velocity in water can be illustrated via the equation below: Z =pV Where: Z = acoustic impedance, p = density of material, V = acoustic velocity It is known the acoustic impedance of water is higher than that of air, meaning ultrasonic waves will have a higher velocity in water than they would in air. If the above equation is rearranged then a higher value for Z will result in a higher value for V, meaning that ultrasonic waves are absorbed at a higher rate in water than in air. However, the most common and perhaps the most beneficial use of ultrasound is throughout the medical field. Ultrasound has been used to image the human body for over 50 years, with the first ultrasound medical diagnostic tool being used by Dr Karl Theo Dussik (Samar, 2010). Ultrasounds are highly useful in a large number of ways, such as the fact that they are not radioactive, are tomographic (can offer cross-sectional views), relatively cheap and images can be acquired in “real time.” Ultrasound utilise the basis of acoustic impedance, as the velocity and absorbance/reflectivity vary dependant on the type of material being assessed, a wide variety of tissues, organs and tumours within the human body can be examined. As the ultrasound waves penetrate the body tissues, some is reflected back to the transducer and some continue to penetrate (V and A, 2010). Ultrasonic transducers allow separate characteristics of these waves to be tested, allowing the individual to alter the frequency and obtain results visually on a waveform generator (i.e. oscilloscope). A detector and an emitter are used to control and determine the number of waves produced, its frequency, amplitude and the max voltage (Vmax). The aim of the experiment is to use the basis of ultrasounds to determine the acoustic impedance of a number of materials, which include: steel, plastic, foam, ceramic tile and a notebook. An ultrasonic wave will be reflected off the materials and the amount reflected will be calculated. This will be then put over the initial max voltage, allowing the percentage of the wave reflected to be found. This value will be R and will vary for each material. The equation below can then be rearranged to find the acoustic impedance of each material R=

(

Z 2−Z 1 Z 2 + Z1

)

Where: R = percentage reflected, Z1 = acoustic impedance of air, Z2 = acoustic impedance of material

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The acoustic impedance of air is known to be 0.000429 and the value for R will be calculated using the ultrasonic transducers. Thus, the acoustic impedance of the certain material can be found by rearranging: −Z 1−Z 1 √ R Z 2= √ R−1 The acoustic impedance of each material will vary and visualise how ultrasounds truly work, utilising the difference between each material to form many images which have been used for countless medical diagnostics.

Materials/Method: Attached an ultrasonic emitter (marked E) to a retort stand with a boss head and clamp. Connected the emitter into Channel 1 of the signal generator. Attached an ultrasonic detector (marked D) to another retort stand with a boss head and clamp and connected to the oscilloscope. Had the emitter and the detector facing one another and set at the same height. Set the distance between the emitter and the detector to be 15 cm. Switched the signal generator on and set it to a sine wave and set the Vpp to 5V. Set the frequency to 40kHz and turned the channel 1 output on. Switched the oscilloscope on and selected AUTO. A sine wave appeared on the screen of the oscilloscope and adjusted the frequency between the range of 35 to 45 kHz until the peak to peak voltage reached a maximum. In this specific experiment, a maximum was reached at 41 kHz. Observed and recorded the Vmax at 15 cm. This was to be the initial Vmax. Once recorded, removed the emitter and placed it on the same retort stand as the detector. Obtained the first material which was to be tested, this was a sheet of steel. Attached the steel onto the retort stand and placed directly in front of the detector and emitter. Adjusted the distance between the detector and emitter and the sheet of steel to be 15 cm (d) and set up as shown below. Once at 15 cm, moved the retort stand in a vertical fashion until a maximum peak to peak voltage was found. Remeasured the distance to assure it was consistently 15cm and recorded the Vmax at the time. Removed the steel and repeated for materials: plastic, tile, foam and a notebook. Attached each material to the retort stand and set the distance between the ultrasonic detector and emitters to be 15cm. Moving each stand until maximum value was shown and recording the Vmax. Once all materials had their Vmax recorded, faced the ultrasonic detectors opposite one another in the exact same fashion they had been initially. However, set the distance to be 20cm. Moved until a maximum peak to peak was shown and recorded the initial Vmax.

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Then set the experiment up as shown in the diagram previously however d = 20cm. Moved the sheet of steel in the range of 20cm until a maximum value was acquired and recorded the Vmax. Repeated for each material, ensuring that the distance was set at 20cm and a maximum peak to peak volume was found before the Vmax was recorded. Recorded the values in two separate tables.

Results: At distance: 15cm Initial Vmax: 44 Material Steel Plastic Tile Foam Notebook

Vmax of Material 35.2 35.2 33.6 28.0 36.8

At distance: 20cm Initial Vmax: 29.6 Material Steel Plastic Tile Foam Notebook

Vmax of Material 28 26.1 24.0 25.6 28.2

Analysis Percent reflected (equation 1): Z 2−Z 1 R= Z 2 + Z1 Rearranged for Z2 (equation 2): −Z 1−Z 1 √ R Z 2= √ R−1

(

)

Know Z1 to equal the acoustic impedance of air which is = 0.000429 R is the amount reflected: R=

Vmax of material Initial Vmax Page 4 of 8

According to the above equations: Steel: R1 = 0.8 R2 = 0.946 Therefore, R average = 0.873 Subbing R and Z1 = 0.000429 into equation 2: Z2 = 0.0126 Pa.s/m3 Plastic: R1 = 0.8 R2 = 0.932 Therefore, R average = 0.866 Subbing R and Z1 = 0.000429 into equation 2: Z2 = 0.0119 Pa.s/m3 Tile: R1 = 0.764 R2 = 0.882 Therefore, R average = 0.823 Subbing R and Z1 = 0.000429 into equation 2: Z2 = 0.00882 Pa.s/m3 Foam: R1 = 0.636 R2 = 0.865 Therefore, R average = 0.751 Subbing R and Z1 = 0.000429 into equation 2: Z2 = 0.00601 Pa.s/m3 Notebook: R1 = 0.836 R2 = 0.953 Therefore, R average = 0.895 Subbing R and Z1 = 0.000429 into equation 2: Z2 = 0.0155 Pa.s/m3

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Acoustic Impedance of Different Materials 0.02 0.02

Acoustic Impedance (Pa.s/m3)

0.01 0.01 0.01 0.01 0.01 0 0 0

Steel

Plastic

Tile

Foam

Notebook

Figure 1.

Discussion: Ultrasonic waves are reflected at boundaries where there is a difference in acoustic impedance (NDT Education Resource Centre). Throughout the experiment, there was a difference in mediums for the ultrasonic waves, as it travelled from air to the material and back through air. This led the initial acoustic impedance to be air and allowed the amount of ultrasonic wave reflected or absorbed to be found. The difference in Z is usually referred to as the impedance mismatch (Delany and Bazley, 1970) and the greater that this mismatch is, the greater the amount percentage of energy that will be reflected will be. As shown in the results (figure 1), the material which had the highest acoustic impedance was the notebook. According to the previous statement, the larger the acoustic impedance, the greater the resistance to the transmission of sound, the more reflected. The smaller the acoustic impedance meaning the less resistant to sound and less will be reflected (Warren, N., 2011). This means that the notebook reflected the most sound back towards the detector and absorbed the least. Thus, if an audible range of sound was being transmitted much an individual would hear a fair bit of it being reflected back to them. Whereas, the lowest acoustic impedance was the foam. This means that more of the ultrasonic wave was absorbed and a considerable amount less was reflected off the material. This makes sense as foam is utilised in numerous sound proofing areas, meaning it has to be an adequate absorbent, otherwise the sound would be merely reflected back.

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There were many variables in the experiment which caused potential error. The measurements were taken with a one metre ruler, already giving away to an uncertainty of ±1cm. Furthermore, this uncertainty was increased as the maximum voltage was attempting to be found. The materials were also a variety of shapes and sizes and although they were placed and attached to the retort stand in a similar fashion, small variations in which the angle the ultrasonic waves struck the material could have had an impact on the amount absorbed. In future experiments, these errors could be avoided by using more accurate measuring equipment and materials which are of the same shape and size. Lasers could be used to ensure that the ultrasonic transducers are facing directly perpendicular to the materials. As if the sound wave is not perpendicular to the surface, some of the sound waves will be reflected away from the transducer (Morgan, 2018). Future experiments could instead use absorption instead of reflection by placing a block of the material in between the two transducers. They could also utilise higher frequencies which have been shown to prove more accurate results (Maris, 1998). Overall, the results which were obtained correlated with the real world acoustic impedances of the materials and depicted the difference of impedance within each material. This impedance is taken advantage of during an ultrasound and the difference is utilised to form an image which is then used for a medical diagnosis.

Conclusion: Ultrasonic waves are utilised in numerous areas, such as nature, the military and medically. Its ability to be absorbed and/or reflected through materials allows it to be so effective. The acoustic impedance varies as the waves travel through different mediums and materials. Due to this independent value, the difference in impedance can be used to map and visualise the human body through imaging. Out of the number of materials tested, the foam was the most absorbent, proving itself as to why it is useful as a soundproofing device. Although there were many variables the materials ranged greatly in acoustic impedance, similar to the human body as the impedance of bone, blood and organs differ. These differences allow the ultrasonic waves to be absorbed or reflected back and through these occurrences, radiologists can successfully map the human body with no radiation, a relatively cheap and effective method.

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References: David, J., Cheek N. (2012), Fundamentals and Applications of Ultrasonic Waves., Broken Sound Parkway, N.W.: CRC Press Delany, M. E. and Bazley, E. N. (1970) ‘Acoustical properties of fibrous absorbent materials’, Applied Acoustics, 3(2), pp. 105–116. Krautkramer, J., Krautkramer, H. and Grabendorfer, W. (1990). Ultrasonic testing of materials. Berlin: Springer-Verlag. Maris, H. (1998) ‘Picosecond ultrasonics’, Scientific American, 278(1), pp. 86–89. doi: 10.1038/scientificamerican0198-86. Morgan, M. (2018). Acoustic impedance | Radiology Reference Article | Radiopaedia.org. [online] Radiopaedia.org. Available at: https://radiopaedia.org/articles/acoustic-impedance [Accessed 8 Jun. 2018]. NDT Education Resource Center 2014, Acoustic Impedance, viewed 8th June 2018

TechTarget, Rouse, M. Ultrasound, viewed 8th June

Warren, N. (2011). Excel HSC physics. Glebe, N.S.W.: Pascal Press, pp.242-248 Wolf, J. (2018). What is acoustic impedance?. [online] Newt.phys.unsw.edu.au. Available at: https://newt.phys.unsw.edu.au/jw/z.html [Accessed 8 Jun. 2018]. XV, C. and A, P. (2010) Atlas of Ultrasound-Guided Procedures in Interventional Pain Managment. Springer New York Dordrecht Heidelberg London.

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