• Level of study

    BAC +2

  • ECTS

    4 credits

  • Component

    Faculty of Science

  • Hourly volume

    36h

Description

The aim of this course is to review various notions of wave physics (D'alembert's equation, progressive 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, in a second time, after having studied the stationary waves it will be a question of studying the interferences (wave tank and other devices) and the physical concepts which are related to them: phase shift, difference of march, condition of constructive interference, destructive interference

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Objectives

  • To know how to 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 by exploiting the families of particular solutions (progressive waves, plane waves, harmonics, stationary solutions)
  • Know how to describe quantitatively the phenomena of wave superposition (interference, beating phenomena, standing waves)
  • Recognize the analogies of propagation phenomena between different topics in physics
  • Know how to establish the propagation equations and their solution in the continuous media approximation
  • Know how to establish the dispersion relation in a dispersive and non-dispersive medium and be able to solve the propagation equations in media with absorption.
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Necessary pre-requisites

This course is intended for students who have already completed the first year of university education. Students who take 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), Newtonian point mechanics.

Recommended prerequisites* : To have studied oscillators, to be at ease with the notions on waves seen in high school.

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Knowledge control

2 CC 25% CT 75%

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Syllabus

- reminder of the 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 formalism of waves: equation of motion, law of behavior, D'alembert's equation, celerity and notion of impedance, energy aspect

- Melde's rope: revisiting the 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 1 dimensional medium.

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

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