The Physics Behind Music

Instructor: B H Suits, Fisher 105.
Text: There is no required text. Many, but not all, of the topics covered can be found in the book "Measured Tones, 2nd Ed." by Ian Johnston (IOP Publishing, 2002), ISBN 0 7503 0762 5 , which you can get from any good quality book vender. A shorter online reference can be found here.

Please report any broken links you find.

Course Description:

PH1090 The Physics Behind Music (3-0-0) f ... 3 Cr

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 ( 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

PH1090 Grades

Your course grade will be based on the combination of your scores for problems* from each class, the hour exams, and final exam grades with the following weights:

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

There is no "curve" of any kind. (That is, it is possible for everyone to get an A ...).

You can estimate your letter grade using the following scheme:

A 86-100        C65-69
AB81-85        CD60-64
B75-80        D55-59
BC70-74        F0-54
(This is for use as a guideline only, adjustments to this scheme may be made when final grades are assigned.)

* "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 The "Midterm Grade," when present, is a current estimate of where you stand.

Auditors - Please Note

If you are an official auditor, please let the instructor know. There is a grade associated with an audit (Satisfactory/Unsatisfactory). If you care about that grade, you will need to find out what you need to do. You will not automatically get a Satisfactory grade.


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"
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
     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
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
     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
*Suggested Readings, where available, should not be expected to cover all the topics listed. Some links may only be available from specific sites and/or may require a subscription.

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Suits Page
MTU Physics Dept