Physics 12a

Waves, Fall 2019


  • Prof. Xie Chen
  • Office: 163 W. Bridge
  • Mail Code: 149-33
  • Phone: x3793
  • Email: xiechen[at]caltech[dot]edu
  • Office Hour: Wednesday, 4:00-5:00pm


  • 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, Oct. 1, 2019

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. Solutions will be posted here.

Each problem set contains a 'Questions and Suggestions' section, from which I hope to gather your feedback about the class. You can ask about things covered or not covered in the lectures; comments and suggestions about the class will be greatly appreciated. I will try to address the questions in class. For the ones that I don't have time to talk about, I encourage you to go to the office hours for discussion.


There will be no mid-term exam, only a final exam. The final exam will be take-home and "limited" open-book.


60% problem sets, 40% final exam.

Recitation and office hour

  • Charles Xu, cxu3[at], Recittion: Annenberg 107, Wed. 2-3pm, Office Hour: Annenberg 2nd floor common area, Wed. 3-4pm
  • Jinrui Hou, jinruihou[at], Recitation + Office Hour: 119 Downs, Tuesday 7-9pm


  • Michael Yao, myao[at], odd homework
  • Yuchen (Dawn) Tang, ytang5[at], even homework


Students will learn about the classical theory of harmonic oscillation and waves, including resonance, normal modes, reflection, interference, diffraction, modulation, polarization, etc.
  • 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, standing 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:

  • 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.
  • 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.
  • Other than the silver bullet, 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.
  • Please put late problem sets in the corresponding grader's mailbox, and email him / her.
  • Late papers make far more work for the graders, who have their own set of pressures and deadlines as students, so please be considerate and ask nicely.

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 up the solution; the work you hand in must be your own.
  • Mathematica will be used occasionally in the homework. It can help with the mathematic chore, but make sure you simplify the result as much as possible to see the physics behind. Do not rely on mathematica to do all your maths.