Wave physics

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

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

• Be able to describe the evolution of a mechanical system subjected to a disturbance by applying local laws (fundamental principle, Kirchhoff's laws, Maxwell's equations).
• Solving a propagation equation by exploiting specific solution families (progressive waves, plane waves, harmonic waves, stationary solutions)
• Be able to quantitatively describe wave superposition phenomena (interference, beating phenomena, standing waves)
• Recognize similarities in propagation phenomena between different topics in physics.
• Know how to establish propagation equations and their solutions in the approximation of continuous media.
• Know how to establish the dispersion relation in a dispersive and non-dispersive medium 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 studies. Students taking this course must have a good command of the following mathematical tools: trigonometric functions, complex numbers (real part, imaginary part, modulus, and argument), scalar and vector products, functions of several variables, derivatives, partial derivatives, primitives, limited development to order 1, and differential equations. They must also have a good command of concepts related to electrokinetics (Kirchoff's laws) and Newtonian mechanics.

Recommended prerequisites*: Have studied oscillators, be familiar with the concepts of waves learned in high school.

2 CC 25% CT 75%

- review of oscillators through the mechanical-electricity analogy

- the concept of waves, propagation medium, inertia, medium cohesion, and wave velocity, energy aspect

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

- Generalized formalism of waves: equation of motion, law of behavior, D'Alembert's equation, velocity and concept of impedance, energy aspect

- Melde's rope: revisiting formalism with the case of the rope

- 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, path difference, constructive interference conditions, destructive interference, etc.