PH1090 - 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:

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.

Extra Examples on Canvas:
Extra examples for some of the more challenging problems are included on Canvas.  These are recorded solutions with commentary.  You are encouraged to view all of these, even if you think you know how to do these problems -- you might gain some extra insight or discover a simpler way to do the problems.

Homework Problems:
Homework problems are at (Canvas) and are available for about 4 days after the corresponding lecture. You may consult others, your notes, ask questions, etc., to successfully complete these problems.  Note, however that very similar problems will appear on the exams and you will not be allowed notes, consultation, etc., for the exams.  These are graded.

Practice problems will be also available on the course pages for additional study. Self-tests are provided for your convenience and are very similar to the homework but are not graded. Note that similar problems may appear on the hour and final exams so these are a good resource for exam study. You will also find practice exam problems in a separate folder as a pdf file.  These are a slightly different format, but provide additional practice.

Hour and Final Exams:
There are two hour exams and a final. The hour exams take the place of 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.  Please study accordingly.

The questions on the exams closely resemble those from the homework and self-tests, both in content and in format.

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 87-100        C 68-71
AB 81-86        CD 64-67
B 76-80        D 60-63
BC 72-75        F 0-59

(This is for use as a guideline only, minor 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 normal and are expected.

Some grades will be visible to you by clicking on the "Grades" tool at the course page at The "Midterm Grade," when and if present, is a progress grade used only for first year students and is only to provide an estimate of current progress.  It has no other meaning or function.

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.

Schedule (Subject to Change)

Week Topics
1 Introduction to Course What is Music? Where did it come from?
What can be studied using methods of the Physicist?
Units/basic definitions
Periodic sounds: Frequency/Period/Pitches
2 Musical Notes, Chords, and Scales
     Musical Intervals, Dissonance, Beats
     Chords and Scales, Logarithms

Combinations of Modes (Superposition, Fourier Series)
     Overtones, Harmonics, "Complex Tones."  Spectra, Pitch perception.

Some simple mechanics (F = ma) and periodic motion
     Mass on Spring



     Driven mass on spring, Quality factor

Other simple oscillators

     Pendulums, Helmholtz resonator, Ocarina,
     Vibrating Strings, air columns

5 More Complex systems  and "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 (in 1-d)
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
8 Ideal Gases
     Microscopic and macroscopic "pictures"
     Sound as a (longitudinal) pressure wave
     Speed of Sound
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
10 Room Acoustics
     reverberation time
     Auditoriums vs. Recording Studios
     Corner Reflectors
11 Room Acoustics con't
     Constructive and Destructive Interference
     Dispersal of waves as an alternative to absorption
     Review for Exam
12 Musical Electronics
  Magnetic Fields and Faraday's Law of Induction
     Microphones, Speakers, Guitar Pick-ups
  Electric Fields and Capacitance
     RC Time Constants
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?)
14 Special Effects, Electronic Music
Review for Final


General Learning Goals:  For areas of physics and music which overlap, students will know and recognize the basic lexicon (definitions, vocabulary, etc), be able to distinguish between measured and perceived quantities, will know basic relationships between quantities for the basic core physics models, and be able to use all of the above to perform simple computations of relevance to music production, performance, and recording.

This course also supports students in achieving University Student Learning Goal #2: Knowledge of the Physical and Natural World. Specific student competencies for this goal can be found under the link for Goal #2 here:

MTU complies with all federal and state laws and regulations regarding discrimination, including the Americans with Disabilities Act of 1990 (ADA). If you have a disability and need a reasonable accommodation for equal access to education or services at MTU, please call the Associate Dean of Students at 487-2212. For other concerns about discrimination, you may contact your advisor, department chair, or the Affirmative Action office.

Suits Page
MTU Physics Dept