Physics 12a

Waves, Fall 2017


  • Prof. Xie Chen
  • Office: 163 W. Bridge
  • Mail Code: 149-33
  • Phone: x3793
  • Email: xiechen[at]caltech[dot]edu
  • Office Hour: Friday, 3:30-4:40pm


  • Math 1abc or equivalent (differential equations, matrices, trigonometry, complex numbers, etc.)
  • Physics 1abc, or equivalent (mechanics, electromagnetism, etc.)
  • Mathematica (basics)


  • Tuesdays 10:30 am - 12:00 am, 269 Lauritsen
  • Thursdays 10:30 am - 12:00 am, 201 Bridge
  • First lecture, Sep. 26, 2017

Recommended Text Book

  • Georgi, The Physics of Waves (free pdf download here)
  • Crawford, Waves (Out of print; free pdf download here)
  • French, Vibrations and Waves
  • The Feynman Lectures, chaps 21-36, 47-51 (can be viewed here)

Problem Sets

Posted below on Thursday of each non-exam week, due on the following Thursday, and returned one week later. Solution sets will be posted on the web.

Each problem set contains a 'Questions and Suggestions' section, from which I hope to gether your feedback about the class. You can ask about things covered or not covered in the lecture; comments and suggestions about the class will be greatly appreciated. I will choose to answer some of the questions in class. For the ones that I don't have time to address, I encourage you to go to the TAs for discussion.


There will be no mid-term exam, only a final exam. The final exam will be take-home and "limited" open-book (only the text and class notes allowed).


60% problem sets, 40% final exam.


  • Kung-Yi Su, ksu[at]caltech, Tuesday 3:00-5:00pm, 119 Downs
  • Min-Feng Tu, minfengtu[at], Wednesday 7:00pm-9:00pm, 107 Downs


  • Kai Klocke, kklocke[at]


  • Introduction, logistics, outline
  • Simple harmonic oscillation: one degree of freedom
  • Forced oscillation and resonance
  • Normal modes: simple harmonic oscillation of more than one degrees of freedom
  • Waves: free and forced oscillation in an infinite system
  • Traveling waves
  • Reflection and transmission
  • Modulations, pulses, and wave packets
  • Waves in two and three dimensions
  • Polarization
  • Interference and Diffraction

Lecture Notes and Problem Sets


OFFICIAL policy:

  • Work (the entire problem set) will be accepted up to one week late at 1/2 credit, no credit thereafter. Please put a note at the top of your problem set if it is late.
  • Students may request extensions from the corresponding grader (see emails above) a day or more in advance. Extension requests are governed by the honor system.
  • One extension (for up to one week) is allowed without question (your silver bullet). Please put a note at the top of your problem set that you are using your silver bullet.
  • Extension requests should be accompanied by a good excuse (eg, physical or mental illness), and in principle should be accompanied by a letter from a doctor or the dean.
  • Please put late or extension problem sets in the corresponding grader's mail box, and email them.
  • Late papers make far more work for the graders, who have their own set of pressures and deadlines as graduate students. There is no entitlement to extensions, so please do not be demanding.

Honor Code and Collaboration Policy

  • Work is governed by the honor system.
  • You may not use sources that contain the answer to a problem or to a very similar problem.
  • In particular, do not use solution sets from previous years, or problem/solution books, at any time. Exams and their solutions from past years are not to be used in any fashion.
  • Discussion with others is encouraged, but then you should go off alone and write it up; the work you hand in must be your own.
  • Mathematica may be used in problem sets, or in exams for getting past some mathematical chore (not for gaining knowledge of the physics). It should never be necessary; it is much better to master the mathematical analysis yourself without help from Mathematica. If you chose to use Mathematica anyway, make sure you simplify the result as much as possible, so that it is easy to see what the math is telling you.