HW6 - ECE 473/TAM 413 Homework Assignment #6 Due: Friday...

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Unformatted text preview: ECE 473/TAM 413 Homework Assignment #6 Due: Friday October 10, 2008 Hour Exam 1: Tuesday, October 14, 2008, 7:00-8:30 pm Hour exams are open book (the text for the course) with one sheet of notes (you can use both sides). Your class notes and lecture notes are not permitted. You can use calculators. Note to graduate students taking the course for 4 hours of graduate credit (NB: only graduate students can receive 4 hours of credit): For the additional 1 hour of credit, you are required to write a paper (typically about 10 pages, double spaced) that discusses in some detail any topic on acoustics for which the fundamentals of engineering acoustics are explicitly described. The paper needs to be based on 5 peer-reviewed publications. The paper will be due Monday, December 5, 2008. However, I must approve the topic and peer-reviewed publications. For the approval process, prepare a one-page outline (including 5 peer-reviewed citations) for submission Monday, October 6, 2008. 1. A 5-kHz plane wave in water at 20C with a peak pressure amplitude of 300 Pa is normally incident on a water-turpentine interface. (a) Determine the transmitted and reflected peak pressure amplitudes. (b) Determine the temporal- average magnitudes of the transmitted and reflected intensity vectors. (c) Determine the sound pressure level of the incident wave relative to 20 Parms. 2. Problem 6.2.2 in Kinsler et al. Use sea water at 13C. 3. Problem 6.3.2 in Kinsler et al. Use fresh water at 20C. 4. Problem 6.4.1 in Kinsler et al. 5. Problem 6.4.2 in Kinsler et al. Use fresh water at 20C for the first medium. 6. Problem 6.4.6 in Kinsler et al. Use sea water at 13C. 7. Problem 6.6.1 in Kinsler et al. Use air at 0C. 8. An acoustic sonar wave is incident from the ocean onto the steel hull of a surface ship. (a) Using the properties for sea water listed in Appendix A10 in the text and the properties of steel listed below, determine all critical angles, i.e., for both longitudinal and transverse (shear) waves, if both exist. Steel: ! o = 7700 kg / m 3 , c l = 6100 m / s and c s = 3280 m / s (b) Determine the angles for all waves transmitted for an incident angle of 20. 9. Show that the energy is conserved between the incident wave and the reflected plus transmitted waves when the incident wave is obliquely incident (15) on an interface between z c two media where z 2 = 1 and c 2 = 1 . 2 3 10. A 500-kHz piezoelectric transducer is made of a material with a density of 2600 kg/m3 and a sound speed of 4400 m/s. It is desired to provide a perfect match to water using a special composite material with a density fixed at 1700 kg/m3 but a sound speed that can be adjusted by changing the composite mixture. (a) What must be the sound speed in the composite and its thickness? (b) With the composite in place, what is the sound power transmission coefficient from the transducer into the water at 700 kHz? (c) What is the sound power transmission coefficient from the transducer to the water without the composite? EXTRA: Try these problems. They will not be graded but the answers will be provided. E1. Problem 6.2.1 (a) (b) (c) in Kinsler et al. Use fresh water and air at 20C. E2. Problem 6.4.3 in Kinsler et al. Use air and hydrogen at 0C. E3. Problem 6.4.4 in Kinsler et al. Use fresh water at 20C. E4. The sound power reflection coefficient is measured as a function of the angle of incidence. Determine the propagation speed and density of the second medium if the first medium (the medium in which the incident wave is propagated) has a characteristic acoustic impedance of 1.96 Mrayls and propagation speed of 1460 m/s. 1.000 Power Reflection Coefficient 0.800 @76.75 0.600 0.400 0.200 0.000 0 10 20 30 40 50 60 70 80 90 Angle of Incidence (degrees) Expanded version of figure: 0.020 Power Reflection Coefficient 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0 10 20 30 40 50 60 70 80 90 0.0144 @69.14 Angle of Incidence (degrees) E5. a) The Scanning Laser Acoustic Microscope (SLAM) is a high-frequency acoustic imaging technique that can be used to determine the propagation speed in a material such as biological tissue. The side view of the SLAM's stage is shown in the figure. Sound is produced by the transducer and propagates at an angle of 45 towards the stage surface through fused silica that has a propagation speed of 5900 m/s. A 200-m thick biological tissue sample is placed on the stage and the transmitted wave propagates through both the biological tissue and the reference saline. When the transmitted wave propagates through the reference saline (propagation speed of 1520 m/s), a specific phase front is incident on the image plan. The microscope can image constant phase front locations. Calculate the lateral shift of the transmitted wave at the image plane that propagates through the reference saline (T = 200 m). b) When the transmitted wave propagates through biological tissue, the lateral shift is increased (relative to the reference saline) by 1.40 m. Calculate the propagation speed in tissue (T = 200 m). Lateral shift T Stage surface Image plane Region where saline and tissue are located 45 c s = 5900 m/s Transducer ...
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This note was uploaded on 09/19/2009 for the course ECE 473 taught by Professor Obrian during the Fall '08 term at University of Illinois at Urbana–Champaign.

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