The Ph.D. qualifying exam in acoustics consists of a four-hour written exam followed by a one-hour oral exam.

## Written Exam

The written exam is 4 hours long, taken in one sitting, and covers 4 subject areas. There are 2 questions per area for a total of 8 questions:

- Physical Acoustics (2 questions)
- Two elective areas of Acoustics (2 questions on each subject area)
- Applied Mathematics (2 questions)

In terms of breadth and depth, the 2 questions on **physical acoustics** cover the course content in Acoustics I and II (ME 384N-1 and ME 384N-2) or their equivalent.

The 4 questions on **acoustics electives** cover 2 subject areas that are selected in advance by the student, with 2 questions on each area. The areas must be selected from the following list:

- Electromechanical Transducers (ME 384N-3)
- Nonlinear Acoustics (ME 384N-4)
- Underwater Acoustics (ME 384N-5)
- Architectural Acoustics (ME 384N-6)
- Ultrasonics (ME 384N-7)
- Vibrations (ME 383Q-1)
- Waves in Elastic Media (e.g., CE 381W Wave Physics)

Course numbers are listed only for guidance; students are not required to have taken any specific courses. For example, a subject area may be selected because the material was covered in a course taken in another department or university.

**Note**: An exception is a subject area in acoustics not covered in this list. As an example, if relevant to the student’s doctoral research, an area in hearing and speech science may be selected, subject to approval, if a faculty member in that program is willing to contribute questions in this area.

The 2 questions on **applied mathematics** test understanding of basic mathematical principles that are commonly encountered in fundamental acoustics. Such principles include solutions of ordinary and partial differential equations, power series solutions, linear independence, elementary linear algebra, determinants, Taylor series, eigenvalue problems, orthogonality, Fourier series and integrals, integration by parts, vector algebra, complex numbers, special functions (e.g., Bessel functions and Legendre polynomials). Examples of topics not covered are contour integration (calculus of residues), general Sturm-Liouville theory, Laplace transforms, numerical methods, perturbation methods.

## Oral Exam

The oral exam is one hour in duration and follows the written exam, normally within a few days. While questions will address the general subject areas covered by the written exam, basic undergraduate principles of mechanical engineering that are pertinent to fundamental acoustics may also be examined.