### 2,208

The number of undergraduate students, 2015-16 school year.

Development of the basic theoretical concepts of acoustical systems; mechanical vibration, plane and spherical wave phenomena in fluid media, lumped and distributed resonant systems, and absorption phenomena and hearing. Course Information: Same as TAM 413. 3 undergraduate hours. 3 or 4 graduate hours. Prerequisite: MATH 285 or MATH 286.

Biomedical Imaging, Bioengineering, and Acoustics

Development of the basic theoretical concepts of acoustical systems; mechanical vibration, plane and spherical wave phenomena in fluid media, lumped and distributed resonant systems, and absorption phenomena and hearing.

Same as: TAM 413

This course is designed for seniors and beginning graduate students in the College of Engineering to deal with the engineering aspects of acoustics.

- Vibrating systems; strings
- Plane waves in fluid media
- Spherical waves in fluid media
- Radiation in fluid media
- Resonators and filters
- Absorption phenomena

This course is designed for seniors and beginning graduate students in the College of Engineering to deal with the engineering aspects of acoustics.

Topics:

- Vibrating systems; strings
- Plane waves in fluid media
- Spherical waves in fluid media
- Radiation in fluid media
- Resonators and filters

Same as: TAM 413

- Differential equations
- Advanced calculus
- Classical mechanics
- Electricity and magnetism

Kinsler, Frey, Coppens, and Sanders, *Fundamentals of Acoustics*, 4th ed., John Wiley & Sons.

Engineering Science: 3 credits

This course is an elective for electrical engineering, computer engineering and theoretical and applied mechanics majors. The goals are to impart the fundamentals of engineering acoustics that constitute the foundation for preparing electrical engineering, computer engineering and theoretical and applied mechanics majors to take follow-on acoustics courses.

**By completion of the course, the students should be able to do the following:**

1. Calculate the displacement and velocity of a second-order mechanical system assuming simple harmonic motion with loss and with forced harmonic excitation. (a)

2. Derive the one-dimensional wave equation for transverse waves on a string. (a)

3. Use the appropriate general solution of the one-dimensional wave equation of the string and solve for the transverse wave function given boundary conditions. (a)

4. Calculate the input mechanical impedance and average input power to a string under forced harmonic excitation. (a)

5. Derive the one-dimensional lossless wave equation for an acoustic wave in a fluid. (a)

6. Calculate the propagation speed in a fluid from the fluid's equation of state and from the fluid's adiabatic bulk modulus and equilibrium density. (a)

7. Derive and solve by separation of variables the three-dimensional acoustic wave equation in a fluid. (a)

8. Calculate energy density and acoustic intensity for both a plane progressive wave and spherical progressive wave in a fluid from any of the first-order propagation quanitities (particle displacement, particle velocity, particle acceleration, excess density, acoustic pressure, condensation, sound pressure level, temperature fluctuation). (a)

9. Derive the pressure reflection coefficient and pressure transmission coefficient using a locally-reacting boundary condition between two fluid media when the incident acoustic wave is normally incident on the boundary. (a)

10. Calculate the pressure reflection coefficient and pressure transmission coefficient between two fluid media when the incident acoustic wave is normally incident on the boundary. (a)

11. Calculate the locations of nodes and antinodes in a standing acoustic wave. (a)

12. Calculate the standing wave ratio (SWR) in a standing acoustic wave. (a)

13. Derive and apply Snell's Law using phase matching conditions. (a)

14. Calculate the pressure reflection coefficient and pressure transmission coefficient between two fluid media when the incident acoustic wave is both normally and obliquely incident on the boundary. (a)

15. Identify the condition for which a critical angle and an angle of intromission exist, and calculate these angles from the fluid properties. (a)

16. Calculate the pressure reflection coefficient and pressure transmission coefficient when an interposed layer of known thickness exists between two media when the incident acoustic wave is normally incident on the boundary. (a)

17. Derive the surface displacement boundary conditions for a radially oscillating sphere in a fluid and derive the propagated acoustic field from this source. (a)

18. Derive the far field acoustic pressure distribution for in-phase continuous line source by applying the field sources from the monopole solution. (a)

19. Calculate the beam width and locations of the sidelobes and nulls from the in-phase continuous line source. (a)

20. Derive the near field (Fresnel) and far field (Fraunhoffer) acoustic pressure distribution for the baffled circular piston source. (a, c)

21. Calculate the on-axis and off-axis acoustic pressure and sidelobes and nulls from the baffled circular piston source. (a)

22. Derive the far field acoustic pressure distribution for the linear array by applying the field sources from the monopole solution. (a, c)

23. Calculate the on-axis and off-axis acoustic pressure and sidelobes, nulls and grating lobes from the linear array source. (a)

24. Engineer arrays so that the grating lobes do not exist. (a)

24. Calculate the resonant frequency in a pipe which has either a rigid or open end, and calculate the total acoustic power radiated under the open-pipe condition. (a)

25. Calculate the intensity reflection coefficient and intensity transmission coefficient in a pipe that has a side branch. This solution models many wind instruments. (a)

26. Derive the acoustic radiation impedance function of a Helmholtz resonator. (a)

1/25/2016by Michael L. Oelze

DEPARTMENT OF ELECTRICAL

AND COMPUTER ENGINEERING

Copyright ©2016 The Board of Trustees at the University of Illinois. All rights reserved