Special relativity (AS.171.207)
Waves (AS.171.201)
Nadia Zakamska
Fall 2014

This is an old webpage; this is not this year's class.


Weekly assignments were posted here and have since been removed from the public domain. The students were also provided with a limited-access link to exams from previous years, so that they could practice. If you are an instructor at another institution and are interested in assigments and exams for this class, please contact N.Z.


Aug 28. Lecture 1. Postulates of special relativity. Derivation of Lorentz transform.
Sept 2. Lecture 2. Length contraction, time dilation.
Sept 4. Lecture 3. Minkowski diagram. Simultaneous events, causally connected events. Transformation of velocity.
Sept 9. Lecture 4. Invariants and 4-vectors. Energy and momentum of particles.
Sept 11. Lecture 5. Forms of energy. Particle collisions.
Sept 16. Lecture 6. Energy and momentum of photons. Doppler effect, aberration.
Sept 18. Lecture 7. Relativistic dynamics. 2nd law of Newton in relativistic case in E&M fields.
Sept 23. Lecture 8. Relativistic particles in electric and magnetic fields. [In Fall 2014 the transformation of E/M fields will likely be an optional lecture in December.]
Beginning of Waves and Oscillations: Expansion of potential near minimum. Simple Harmonic oscillator.
Sept 25. Lecture 9. Damped harmonic oscillator. Complex numbers. (Morin Chapter 1.)
Sept 30. Midterm 1. Special Relativity midterm based on lectures 1-8. Books, calculators, notes are OK.
Oct 2. Lecture 10. Driven harmonic oscillator. Resonance curve.
Oct 7. Lecture 11. Beats. Coupled oscillations. (Morin chapter 2)
Oct 9. Lecture 12. Longitudinal vs transverse oscillations (Morin chapter 4.1). Normal modes. (Morin chapter 2)
Oct 16. Lecture 13. Wave equation.
Oct 21. Lecture 14. Discrete real Fourier series. (Morin chapter 3)
Oct 23. Lecture 15. Discrete complex Fourier series. Response of RLC circuits to periodic voltage. Fourier transforms. Response of RLC circuits to arbitrary voltage.
Oct 28. Lecture 16. Delta function. Relationship between Fourier transforms and Fourier series. Aliasing, strobe effect, Nyquist theorem.
Oct 30. Lecture 17. Standing vs traveling waves (Morin chapter 4.2). Reflection and transmission.
Nov 4. Lecture 18. Impedance. Energy and momentum of waves (Morin Ch 4). Attenuation (Morin Ch 4).
Nov 6. Lecture 19. Sound waves (Morin Ch 5). Euler and continuity equations. Sound speed in solids and gases. Energy of the sound.
Nov 11. Lecture 20. Non-relativistic Doppler effect. Musical instruments (Morin Ch 5). Fixed and open boundary conditions.
Nov 13. Lecture 21. Amplitude of 2D and 3D waves. Dispersion (Morin Chapter 6). Wave packets, group velocity, phase velocity. Break-down of wave approximation, high-frequency cut-off, dispersion relation, evanescent waves, penetration length.
Nov 18. Midterm 2. Everything up to and including Lecture 17. Open book exam.
Nov 20. Lecture 22. Dispersion: example problems. Boundary effects and interference (Morin Chapter 9). 2D and 3D wave equation. Huygens - Fresnel principle. Reflection and refraction. Snell's law.
Dec 2. Lecture 23. Double-slit interference. Multi-slit interference.
Dec 4. Lecture 24. Single-slit diffraction. Single-slit effects in interference. [Brief intro to polarization.]


Ripple tank simulator (and lots of other simulations on the parent webpage) [If you are encountering issues running this app on Mac, use Safari and check Java security settings, as described here.]

Torsional pendulum simulation [If it is not running, use the same Java fix as above.]

CGS vs MKS (scroll down for a conversion table for electromagnetic units)

Tacoma Narrows video

Tuned mass damper

Course information

1. Overview
Special Relativity and Waves is the third course in the four-semester introductory sequence for physics majors. The course is divided into two parts. In the first three-four weeks we study the theory of special relativity (this is where 171.207 course ends after the first midterm and relevant homework). Then the rest of the semester is devoted to the physics of waves (for those who take the full course 171.201). The course builds upon the background in classical mechanics and electromagnetism, and precedes the full development of quantum physics. The course is calculus-based and uses differential equations, complex numbers and matrices. An introduction to complex numbers is included in the course. The use of matrices is optional but highly desired, here is a quick refresher.

2. Lecture schedule
Instructor: Prof. Nadia Zakamska
Lectures: Tue/Thur, 10:30-11:45 am (some exceptions possible), Bloomberg 361; office hours: after the class

3. Sections and labs
The Thursday sections will be either laboratory exercises or problem discussions. The discussion sections have the standard duration of 0h50min, but 1h30min is allocated for the laboratory exercises. Schedule of labs vs sections is here (the default option is a regular section).
Section 1: Prasenjit Bose, Bloomberg 478, Thur 1:30-3:00 pm lab days, Thur 1:30-2:20 pm section days, office hours: Friday 3:00-4:15 PUC lab, email: pbose(at)pha.jhu.edu
Section 2: David Rivas, Bloomberg 478, Thur 3:00-4:30 pm lab days, Thur 3:00-3:50 pm section days, office hours: Friday 4:15-5:30 PUC lab, email: drivas1(at)jhu.edu
With the exception of the first lab on Special Relativity, which can be done individually, the experimental part of the labs will be done in pairs. You are welcome to use the Special Relativity lab to find a lab partner.
Software necessary for Lab 2 and beyond is available here. Mathematica would be very useful as well; some resources for working with Mathematica available here.

4. Grades
30% homework assignments and lab reports
30% midterms (Midterm 1 on Special Relativity is on Sept 30; Midterm 2 TBD)
40% final exam (Dec 12, Friday, 9 am -- noon, Bloomberg 361)
Homework and exam policy is here.

5. Textbooks
Recommended book for the first part of the course: "Introduction to Special Relativity" by Resnick
Main book for the second part of the course: Harvard Waves course by David Morin, used with his kind permission (scroll down to find "Works in progress")
Recommended book for the second part of the course: "Vibrations and Waves" (MIT intro series) by A.P.French
A limited-access link to practice problems, old exams and additional electronic resources will be provided at the first lecture.