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 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|
* "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" *|
Introduction to Course
What is Music? Where'd it come from?
What can be studied using methods of the Physicist?
Periodic sounds: Frequency/Period/Pitches
Wikipedia Entries for "Music"
Stone Age Flute (Nature, Dec 17, 2004)
NPR Bird Song Story
Radio Lab Show #202
Musical Notes, Chords, and Scales
Musical Intervals, Dissonance, Beats
Chords and Scales, Logarithms
See "Scales" and related sub-sections
NPR Physics of Music Story
Some simple mechanics (F = ma) and periodic motion
Pendulum/Mass on Spring
Stretched String - Wavelengths
Laws of Motion (Wikipedia)|
Simulation applets - Masses & Springs and Wave on a String
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|
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
Attack and Release of pitches
Strike tones and other non-resonant noises
"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
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
Coupling of sound between instruments and Air
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
Auditoriums vs. Recording Studios
Reverberation Time (Wikipedia)|
2-D wave Applet ("ripple tank")
3-D wave Applet
Room Acoustics con't
Constructive and Destructive Interference
Dispersal of waves as an alternative to absorption
Review for Exam
Cox Diffuser Paper
Cox and D'Antonio Concert Hall Acoustics paper
Magnetic Fields and Faraday's Law of Induction
Microphones, Speakers, Guitar Pick-ups
Electric Fields and Capacitance
RC Time Constants
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
Special Effects, Electronic Music
Review for Final