Special relativity (AS.171.207)
Waves (AS.171.201) Nadia Zakamska Fall 2015 |

This is a webpage for FALL 2015. All materials have been removed in preparation for the next class in FALL 2016. |

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 or by appointment.

**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). The schedule is **tentative**.

Section 1: David Rivas, Bloomberg 478, Thur 1:30-3:00 pm lab days, Thur 1:30-2:20 pm section days, office hours: Fridays 3:00-5:00 pm in Bloomberg 259, email: drivas1(at)jhu.edu

Section 2: Mike Valentine, Bloomberg 478, Thur 3:00-4:30 pm lab days, Thur 3:00-3:50 pm section days, office hours: Mondays 3:00-5:00 pm in Bloomberg 259, email: mvalen16(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 useful as well; it is free for JHU students (see instructions here), and Wolfram has resources on their website to get you started.

**4. Grades**

30% homework assignments and lab reports

30% midterms (Midterm 1 on Special Relativity 10/01; Midterm 2 date TBD)

40% final exam (Dec 11, Friday, 9 am -- noon, Bloomberg 361)

Homework and exam policy is here.

**5. Textbooks**

Complete lecture notes by N. Zakamska on Special Relativity are now publicly available here (new as of Nov 2015).

Recommended book for Special Relativity: "Introduction to Special Relativity" by Resnick

Main book for Waves: Harvard Waves course by David Morin, used with his kind permission (scroll down to find "Works in progress")

Recommended book for Waves: "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.

Assignments |

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.

Syllabus |

Aug 27. Lecture 1. Postulates of special relativity. Derivation of Lorentz transform.

Sept 1. Lecture 2. Length contraction, time dilation.

Sept 3. Lecture 3. Minkowski diagram. Simultaneous events, causally connected events. Transformation of velocity.

Sept 8. Lecture 4. Invariants and 4-vectors. Energy and momentum of particles.

Sept 10. Lecture 5. Forms of energy. Particle collisions.

Sept 15. Lecture 6. Energy and momentum of photons. Doppler effect, aberration.

Sept 17. Lecture 7. Relativistic dynamics. 2nd law of Newton in relativistic case in E&M fields.

Sept 22. Lecture 8. Relativistic particles in electric and magnetic fields.
**Beginning of Waves and Oscillations**: Expansion of potential near minimum. Simple Harmonic oscillator.

Sept 24. Lecture 9. Damped harmonic oscillator. Complex numbers. (Morin Chapter 1.)

Sept 29. Lecture 10. Driven harmonic oscillator.
**Oct 1. Midterm 1. Special Relativity midterm based on lectures 1-8. Books, calculators, notes are OK.**

Oct 6. Lecture 11. Resonance curve. Beats.

Oct 8. Lecture 12. Coupled oscillations: two, three masses (Morin chapter 2). Longitudinal vs transverse oscillations (Morin chapter 4.1). Normal modes (Morin chapter 2).

Oct 13. Lecture 13. Coupled oscillations: N masses.

Oct 20. Lecture 14. Discrete real Fourier series. (Morin chapter 3)

Oct 22. Lecture 15. Discrete complex Fourier series. Response of RLC circuits to periodic voltage. Fourier transforms. Response of RLC circuits to arbitrary voltage.

Oct 27. Lecture 16. Delta function. Relationship between Fourier transforms and Fourier series. Aliasing, strobe effect, Nyquist theorem. Wave equation.

Oct 29. Lecture 17. Standing vs traveling waves (Morin chapter 4.2). Reflection and transmission.

Nov 3. Lecture 18. Impedance. Energy and momentum of waves (Morin Ch 4).

Nov 5. Lecture 19. Attenuation (Morin Ch 4). Sound waves (Morin Ch 5). Euler and continuity equations. Sound speed in solids and gases.

Nov 10. Lecture 20. Energy of the sound. Non-relativistic Doppler effect. Musical instruments (Morin Ch 5). Fixed and open boundary conditions.

Nov 12. Lecture 21. Amplitude of 2D and 3D waves. Dispersion (Morin Chapter 6). Wave packets, group velocity, phase velocity. Break-down of the wave approximation, high-frequency cut-off, dispersion relation, evanescent waves, penetration length.
**Nov 17. Midterm 2. Everything up to and including Lecture 19. Open book exam. **

Nov 19. 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 1. Lecture 23. Double-slit interference. Multi-slit interference.

Dec 3. Lecture 24. Single-slit diffraction. Single-slit effects in interference. Diffraction limit in astronomical instrumentation.

Miscellaneous |

Ripple tank simulator (and lots of other simulations on the parent webpage) [I have encountered issues running this ap on a Mac. I have updated my Java to the most current version, which ruined it for Chrome, but works on Safari, and I set the security settings to minimal.]

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)

Albert Michelson's mechanical harmonic analyzer (I recommend the first three videos: Intro, Synthesis, Analysis.)

Coffee waves, quantum mechanics and Bessel functions

Decomposing a square wave into a Fourier series

1D, 2D and 3D standing waves: Linear Ruben's tube, Ruben's square, Standing waves in a 2D soap film.