Physics concepts and methods associated with musical instruments, musical recording, and musical acoustics are discussed at an introductory level. Topics which can be expected include periodic motion, normal modes and resonance, superposition and Fourier series, waves, sound and acoustics, magnetism and electromagnetic induction, and topics from non-linear physics.
Prerequisite: Calculus ready
For the most up-to-date catalog copy, go to the MTU Catalog
If you need to be absent (for "excusable" reasons) contact your instructor to make up the missed work. If possible, make arrangements ahead of time. See the MTU student handbook section on policies for examples of excused absences.
In Class Problems:
During most classes there will be a few
problems for you to do which are handed in at the end of class and which are graded. You are encouraged to ask for help, consult others, etc., to successfully complete these problems.
Homework Problems:
Homework problems are on blackboard (www.courses.mtu.edu) and are available for about 4 days after the corresponding lecture. These are graded.
Practice problems will be also available on the course pages at for additional study. Self-tests are similar to the homework but are not graded. Note that similar problems may appear on the hour and final exams. You will also find practice exam problems in a separate folder as a pdf file.
Hour and Final Exams:
There are two hour exams and a final. The hour exams take place during a normal class period. Consult MTU's final exam schedule for the time and location for the 2 hour comprehensive final.
No notes, consultation, etc., are allowed for the exams
| Sum of all problems* (as a percentage) | 1/3 |
| Hour exam 1 | 1/6 |
| Hour exam 2 | 1/6 |
| Final Exam (out of 100) | 1/3 |
| A | 86-100 | C | 65-69 | |
| AB | 81-85 | CD | 60-64 | |
| B | 75-80 | D | 55-59 | |
| BC | 70-74 | F | 0-54 |
* "Problems" includes the in class problems and the online homework problems. Please also note that for the problems, which are open notes, etc., scores greater than 90% are expected.
Some grades will be visible to you by clicking on the "My Grades" tool at the course page at www.courses.mtu.edu. The "Midterm Grade," when present, is a current estimate of where you stand.
| Week | Topics | Some Suggested "Readings" * |
|---|---|---|
| 1 |
Introduction to Course
What is Music? Where'd it come from? What can be studied using methods of the Physicist? Units/basic definitions Periodic sounds: Frequency/Period/Pitches |
Wikipedia Entries for "Music"
and
"Prehistoric Music" Stone Age Flute (Nature, Dec 17, 2004) NPR Bird Song Story Radio Lab Show #202 |
| 2 |
Musical Notes, Chords, and Scales Musical Intervals, Dissonance, Beats Chords and Scales, Logarithms |
See "Scales" and related sub-sections
here. NPR Physics of Music Story |
| 3 |
Some simple mechanics (F = ma) and periodic motion Pendulum/Mass on Spring Stretched String - Wavelengths |
Newton's
Laws of Motion (Wikipedia) Simulation applets - Masses & Springs and Wave on a String |
| 4 |
Resonance String (con't) driven by sinusoidal source Vibrations in an Air column (and wind instruments) Combinations of Modes (Superposition, Fourier Series) Overtones, Harmonics, "Complex Tones." |
Simulation applets - Fourier: Making Waves |
| 5 |
More Complex Normal Modes Xylophone Bars and Tubular Chimes Real Strings (and why piano tuning is an art) Drum Head (demo and computer simulation), Church Bells Traveling Waves (1-d) |
Acoustic Simulation Applets Vibrations of Hand Bells |
| 6 |
Attack and Release of pitches Strike tones and other non-resonant noises "Uncertainty Principle" (EXAM) |
|
| 7 |
Non-linear Systems "Simple" model for a clarinet, bowed string ("self-driven" systems) Interesting solutions of non-linear physics problems The ascending/descending Chinese Gong Start of ideal gases. Atoms, Molecules, Phases of Matter Pressure, Temperature, Volume, Gas Laws |
J. Acoust. Soc. 74, 1325 (1983) [a bit technical] The Atom (Am. Nuc. Soc.) Atoms and Molecules Interactive Periodic Table |
| 8 |
Ideal Gases Microscopic and macroscopic "pictures" Sound as a (longitudinal) pressure wave Speed of Sound |
PhET Ideal Gas Java Applet PhET Sound Java Applet Ideal Gas Summary |
| 9 |
Loudness (decibels) Coupling of sound between instruments and Air Acoustic Impedance How much sound gets out? Intensity vs distance Wave Propagation in 2- and 3-d |
Multipole radiation animations Acoustic Impedance Defined Acoustic Impedance in Wikipedia |
| 10 |
Room Acoustics reverberation time Reflection/Absorption Auditoriums vs. Recording Studios Corner Reflectors |
Reverberation Time (Wikipedia) 2-D wave Applet ("ripple tank") 3-D wave Applet |
| 11 |
Room Acoustics con't Constructive and Destructive Interference Dispersal of waves as an alternative to absorption Review for Exam (EXAM II) |
Cox Diffuser Paper Cox and D'Antonio Concert Hall Acoustics paper |
| 12 |
Musical Electronics Magnetic Fields and Faraday's Law of Induction Microphones, Speakers, Guitar Pick-ups Electric Fields and Capacitance Microphones RC Time Constants |
Faraday's
Law (Wikipedia) Microphones (Wikipedia) |
| 13 |
Musical Electronics (con't) Cables and Shielding Audio Recording Methods Magnetic recording, optical recording. A to D and D to A (what is it?) |
Magnetic Recording (Wikipedia) Recording Technology History |
| 14 |
Special Effects, Electronic Music Review for Final |
|
| - | FINAL EXAM |