Wave physics

The aim is to review various notions of wave physics (D'alembert's equation, travelling waves, standing waves, reflection, transmission) through the study of different physical systems: mechanical (spring, string, acoustic...), electrical (telegraph line, co-axial...) or electromagnetic, and to arrive at a general formalism for the study of linear wave phenomena.

Then, after studying standing waves, we'll move on to studying interference (wave tank and other devices) and the related physical concepts: phase shift, step difference, constructive interference condition, destructive interference...

• Describe the evolution of a mechanical system subjected to a disturbance by applying local laws (fundamental principle, Kirchoff's laws, Maxwell's equations).
• Solve a propagation equation using specific families of solutions (progressive, plane, harmonic waves, stationary solutions)
• Quantitative description of wave superposition phenomena (interference, beat phenomena, standing waves)
• Recognize the analogies of propagation phenomena between the different themes of physics
• Know how to establish propagation equations and their solutions in the continuous media approximation
• Know how to establish the dispersion relation in dispersive and non-dispersive media, and be able to solve propagation equations in media with absorption.

This course is designed for students who have already completed the 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, derivative, partial derivative, primitive, limited development to order 1 and differential equations. They must also master concepts related to electrokinetics (Kirchoff's laws) and Newtonian point mechanics.

Recommended prerequisites* : Have studied oscillators, be familiar with wave concepts from high school.

2 CC 25% CT 75%

- reminder of oscillators through the mechanical-electrical analogy

- the notion of wave, propagation medium, inertia, cohesion of the medium and celerity of a wave, energy aspect

- the telegrapher's equation and D'Alembert's equation

- generalized wave formalism: equation of motion, law of behavior, D'alembert equation, celerity and notion of impedance, energy aspect

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

- reflection and transmission of a wave

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

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

- waves and interference (wave tank and other devices): phase shift, step difference, constructive interference condition, destructive interference...