Wave Physics

The first step is to review various concepts in wave physics (D'Alembert’s equation, traveling waves, standing waves, reflection, transmission) through the study of various physical systems—mechanical (springs, strings, acoustics...), electrical (telegraph lines, coaxial cables, etc.), or electromagnetic systems, and to arrive at a general framework for the study of linear wave phenomena.

Next, after studying standing waves, we will examine interference (wave tanks and other devices) and the related physical concepts: phase shift, path difference, conditions for constructive interference, and destructive interference.

• Be able to describe the behavior of a mechanical system subjected to a disturbance by applying local laws (fundamental principle, Kirchhoff's laws, Maxwell's equations).
• Solve a propagation equation by using families of particular solutions (traveling waves, plane waves, harmonic waves, stationary solutions)
• Be able to quantitatively describe the phenomena of wave superposition (interference, beats, standing waves)
• Recognize the similarities in propagation phenomena across different topics in physics
• Be able to derive propagation equations and solve them using the continuous media approximation
• Understand how to derive the dispersion relation in dispersive and nondispersive media and be able to solve propagation equations in media with absorption.

This course is intended for students who have already completed their first year of university-level study. Students taking this course must have a solid grasp of the following mathematical concepts: trigonometric functions, complex numbers (real part, imaginary part, modulus, and argument), scalar and vector products, functions of several variables, derivatives, partial derivatives, integrals, first-order series expansions, and differential equations. They must also have a solid grasp of concepts related to electrokinetics (Kirchhoff’s laws) and Newtonian point mechanics.

Recommended prerequisites*: Have studied oscillators; be familiar with the concepts related to waves covered in high school.

2 CC 25% CT 75%

- A review of oscillators using the mechanics-electricity analogy

- the concept of a wave, the medium through which it propagates, inertia, the cohesion of the medium, the speed of a wave, and energy-related aspects

- the telegraph operator's equation and D'Alembert's equation

- Generalized formalism of waves: equation of motion, behavioral law, D'Alembert's equation, speed of propagation, and the concept of impedance; energy aspects

- Melde's rope: a reinterpretation of formalism using the rope as an example

- reflection and transmission of a wave

- Acoustic waves: acoustic wave equation, impedances, Doppler effect, shock wave—Mach cone.

- standing waves: 1 boundary condition, 2 boundary conditions in a one-dimensional medium.

- Waves and interference (wave tank and other devices): phase shift, phase difference, conditions for constructive interference, destructive interference...