Wave propagation

General presentation of wave phenomena through acoustic, electromagnetic and microwave waves.

• Understand the concepts of waves and the physical phenomena that govern them
• Know how to manipulate waves, notions of propagating/stationary waves
• Establish the equations of wave propagation, whether acoustic, electromagnetic or on microwave lines, solve these equations
• Know the notions of impedance and impedance matching
• To know the phenomena of reflection, transmission, attenuation
• Discover the notions of propagation in energy potentials and their resolution (Schrödinger equation)
• Understand concrete applications of acoustic, electromagnetic and microwave waves

Required Prerequisites:

Electrostatics and magnetostatics, electric and magnetic fields

Basic geometrical optics

Mathematical concepts: complex, Fourier transform...

Recommended prerequisites:

Electrostatics and magnetostatics, electric and magnetic fields

Basic geometrical optics

Mathematical concepts: complex, Fourier transform...

final control 70% + 30% TP

Acoustic waves. 12 hrs CM, 10,5 hrs td

1. Introduction : Generalities on wave phenomena
2. Acoustic Waves / Sound waves; Plane waves, travelling/stationary waves
3. Propagation of waves in a one-dimensional medium, propagation equation of pressure waves, waves on a string.
4. Reflection and transmission phenomena: Impedance
5. Properties of acoustic waves and associated applications (ultrasonography, sonar, ...).
6. Doppler effect and applications to velocimetry.
7. Example of applications of the interaction Waves - Matter in medical environment

Microwave waves. CM 12h. TD 6 h, TP 9h

1. Introduction
2. Microwaves in the electromagnetic spectrum
3. The electromagnetic spectrum
4. Characteristic properties of microwaves
5. Reminders (mathematics, electricity, power, dB)
6. Localization of energy in space
7. Power transmission by idealized line
8. The electromagnetic wave T.E.M guided by a line
9. Voltage wave and current wave
10. Characteristic resistance of the line
11. Reflection phenomenon at the end of the line
12. Reflection factor
13. Evolution of the voltage at the ends of a line
14. Table method
15. The transmission lines in harmonic regime
16. Linear parameters
17. Equation of the lines (equation of the telegraphers)
18. Resolution in the case of negligible losses (equation of the radioelectricians)
19. General solution in harmonic regime
20. Characteristic impedance, phase and attenuation constants
21. Study of lossless transmission lines
22. Propagation of undamped sine waves
23. Voltage and current distribution along the line
24. Impedance at each point of the line
25. Reflection factor and impedance
26. Standing wave ratio
27. Maximum and minimum value positions
28. Standing wave ratio 

Wave physics. CM 9h, TD 9h

1. Wave-Corpuscle Duality

            1.1 Classical physics in the 19th century

            1.2 Towards mechanics

            1.3 The Wave-Corpuscle duality

2. Schrödinger equation for the free particle

            2.1 Schrödinger's equation

            2.2 Quantum mechanical postulates

            2.3 Spatial equation by separation of variables

            2.4 Operators in Quantum Mechanics

            2.5 Boundary conditions

            2.6 Typical approach

3. Scattering by a potential in space

            3.1 Finite potential well

            3.2 Potential walk

            3.3 Potential barrier