Special relativity (AS.171.207)
Waves (AS.171.201) Nadia Zakamska Fall 2017 |

**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: 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: Derek Brehm, Bloomberg 478, Thur 1:30-3:00 pm lab days, Thur 1:30-2:20 pm section days, office hours: Mondays 2:00-4:00 pm in Bloomberg 478, email: brehm.derek(at)gmail.com

Section 2: David Rivas, Bloomberg 478, Thur 3:00-4:30 pm lab days, Thur 3:00-3:50 pm section days, office hours: Fridays 1:00-3:00 pm in Bloomberg 478, 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.

Loggerpro is software necessary for Lab 2 and beyond. Access instructions will be emailed to the class toward the end of September. 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 (dates: Oct 3 and Nov 7, see also schedule above)

40% final exam (Monday Dec 18, 9 am -- noon, **this date and time are set by the registrar and I cannot change it**)

Homework and exam policy is here.

**5. Textbooks**

Main book for Special Relativity: N.L.Zakamska's lecture notes, available here. Please report any typos to the instructor.

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 |

Sept 5. Lecture 1. Postulates of special relativity. Derivation of Lorentz transform.

Sept 7. Lecture 2. Length contraction, time dilation.

Sept 12. Lecture 3. Minkowski diagram. Simultaneous events, causally connected events. Transformation of velocity.

Sept 14. Lecture 4. Invariants and 4-vectors. Energy and momentum of particles.

Sept 19. Lecture 5. Forms of energy. Particle collisions.

Sept 21. Lecture 6. Energy and momentum of photons. Doppler effect, aberration.

Sept 26. Lecture 7. Relativistic dynamics. 2nd law of Newton in relativistic case in E&M fields.

Sept 28. Lecture 8. Relativistic particles in electric and magnetic fields.
**Oct 3. Midterm 1 -- Special Relativity **
**Waves and Oscillations**: Expansion of potential near minimum. Simple Harmonic oscillator.

Oct 5. Lecture 9. Damped harmonic oscillator. Complex numbers. (Morin Chapter 1.)

Oct 10. Lecture 10. Driven harmonic oscillator. Resonance curve.

Oct 12. Lecture 11. Beats. Coupled oscillations: two, three masses (Morin chapter 2).

Oct 17. Lecture 12. Longitudinal vs transverse oscillations (Morin chapter 4.1). Normal modes (Morin chapter 2).

Oct 19. Lecture 13. Coupled oscillations: N masses.

Oct 24. Lecture 14. Discrete real Fourier series (Morin chapter 3) for functions defined on an interval. Oscillations of strings fixed at both ends.

Oct 26. Lecture 15. Fourier series for periodic functions. Discrete complex Fourier series. Response of RLC circuits to periodic voltage.

Oct 31. Lecture 16. Fourier transforms. Response of RLC circuits to arbitrary voltage.

Nov 2. Lecture 17. Delta function. Relationship between Fourier transforms and Fourier series. Aliasing, strobe effect, Nyquist theorem.
**Nov 7. Midterm 2** on everything up to and including Lecture 17.

Nov 9. Lecture 18. Wave equation. Standing vs traveling waves (Morin chapter 4.2).

Nov 14. Lecture 19. Reflection and transmission. Impedance. Energy and momentum of waves (Morin Ch 4). Attenuation (Morin Ch 4).

Nov 16. Lecture 20. Sound waves (Morin Ch 5). Euler and continuity equations. Sound speed in solids and gasses. Energy of the sound.

Nov 21, Nov 23 -- Thanksgiving break

Nov 28. Lecture 21. Non-relativistic Doppler effect. Musical instruments. Fixed and open boundary conditions. Amplitude of 2D and 3D waves. Dispersion (Morin Chapter 6). Wave packets, group velocity, phase velocity.

Nov 30. Lecture 22. Dispersion: Break-down of the wave approximation, high-frequency cut-off, dispersion relation, evanescent waves, penetration length, example problems.

Dec 5. Lecture 23. Boundary effects and interference (Morin Chapter 9). 2D and 3D wave equation. Huygens - Fresnel principle. Reflection and refraction. Snell's law. Double-slit interference.

Dec 7. Lecture 24. Multi-slit interference. 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 Firefox, 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.

Learning goals |

By the end of this course, the students will be able to:

-- Solve standard problems in Special Relativity up to and including relativistic dynamics and apply 4-vector formalism;

-- Conduct table-top experiments using mechanical and optical setups and design and apply models to quantitatively explain the experimental results;

-- Apply advanced mathematical apparatus (differential equations, Fourier analysis, complex numbers) to solve problems on waves and oscillations in physical systems drawn from the introductory sequence on mechanics and electromagnetism;

-- Recognize complex wave phenomena, such as dispersion, diffraction and interference, and analyze them in idealized contexts.