| Special relativity (AS.171.207)
Waves (AS.171.201) Nadia Zakamska Fall 2013 |
| This is an old course webpage for information only, not a currently active course. Some materials have been removed in preparation for the next class. |
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.
There is a lab instead of a regular session roughly every other week. 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.
Course information and week-by-week schedule removed by instructor (08-27-2014) to avoid confusion with the Fall 2014 information and schedule.
The webpage for the previous year's class is here. Software necessary for Lab 2 and beyond is available here. Some resources for working with Mathematica available here.
| 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 3. Lecture 1. Postulates of special relativity. Derivation of Lorentz transform.
Sept 5. Lecture 2. Length contraction, time dilation.
Sept 10. Lecture 3. Minkowski diagram. Simultaneous events, causally connected events. Transformation of velocity.
Sept 12. Lecture 4. Invariants and 4-vectors. Energy and momentum of particles.
Sept 17. Lecture 5. Energy and momentum of photons. Particle collisions. Doppler effect, aberration.
Sept 19. Lecture 6. Relativistic dynamics. 2nd law of Newton in relativistic case in E&M fields.
Sept 24. Lecture 7. Introduction to transformation of E/M fields. Validity of special relativity.
Sept 26. Lecture 8. Expansion of potential near minimum. Simple harmonic oscillator. Damped harmonic oscillator. Complex numbers. (Morin Chapter 1.)
Oct 1. Midterm 1. Special Relativity midterm based on lectures 1-7. Books, calculators, notes are OK.
Oct 3. Lecture 9. Driven harmonic oscillator. Resonance curve.
Oct 9. Lecture 10. Beats. Coupled oscillations. (Morin chapter 2)
Oct 11. Lecture 11. Longitudinal vs transverse oscillations (Morin chapter 4.1). Normal modes. (Morin chapter 2)
Oct 17. Lecture 12. Wave equation.
Oct 22. Lecture 13. Discrete real Fourier series. (Morin chapter 3)
Oct 24. Lecture 14. Discrete complex Fourier series. Response of RLC circuits to periodic voltage.
Oct 29. Lecture 15. Fourier transforms. Response of RLC circuits to arbitrary voltage. Delta function. Relationship between Fourier transforms and Fourier series.
Oct 31. Lecture 16. Aliasing, strobe effect, Nyquist theorem. Standing vs traveling waves (Morin chapter 4.2).
Nov 5. Midterm 2. Based on lectures 1-15; no more than one special relativity problem. Open notes / open book / calculator OK.
Nov 7. Lecture 17. Reflection and transmission. Impedance.
Nov 12. Lecture 18. Energy and momentum of waves (Morin Ch 4). Attenuation (Morin Ch 4). Sound waves (Morin Ch 5).
Nov 14. Lecture 19. Euler and continuity equations. Sound speed in solids and gases. Energy of the sound.
Nov 19. Lecture 20. Non-relativistic Doppler effect. Musical instruments (Morin Ch 5). Amplitude of 2D and 3D waves. Polarization.
Nov 21. Lecture 21. 2D and 3D wave equation. EM wave equation. Boundary effects and interference (Morin Chapter 9). Huygens - Fresnel principle. Reflection and refraction. Snell's law. Double-slit interference. Multi-slit interference.
Nov 26. Lecture 22. Single-slit diffraction. Single-slit effects in interference. Dispersion (Morin Chapter 6). Wave packets, group velocity, phase velocity. Break-down of wave approximation, high-frequency cut-off, dispersion relation.
Dec 3. Lecture 23 / Lab 6. Low-frequency cut-off, high-frequency cutoff, evanescent waves, penetration length.
Dec 5. Lecture 24. [Some advanced stuff: dispersion relation of cold plasma, dispersion of pulsar signals in interstellar space, reflection of radio waves off the ionosphere.]
| Miscellaneous |
Ripple tank simulator (and lots of other simulations on the parent webpage)
CGS vs MKS (scroll down for a conversion table for electromagnetic units)