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, and solve these equations.
• Understand the concepts of impedance and impedance matching
• Know the phenomena of reflection, transmission and attenuation
• Discover the concepts of propagation in energy potentials and their resolution (Schrödinger equation)
• Understand concrete applications of acoustic, electromagnetic and microwave waves

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 examination 70% + 30% practical work

Acoustic waves. 12 h CM, 10.5 h td

1. Introduction: General principles of wave phenomena
2. Acoustic waves / Sound waves; plane waves, traveling/stationary waves
3. Wave propagation in a one-dimensional medium, pressure wave propagation equation, waves on a string.
4. Reflection and transmission phenomena: Impedance
5. Acoustic wave properties and associated applications (ultrasonography, sonar, etc.).
6. Doppler effect and applications to velocimetry.
7. Examples of applications of wave-matter interaction in the medical field

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

1. Introduction
2. Microwaves in the electromagnetic spectrum
3. The electromagnetic spectrum
4. Characteristic microwave properties
5. Reminders (mathematics, electricity, power, dB)
6. Locating energy in space
7. Idealized line power transmission
8. The T.E.M. electromagnetic wave guided by a line
9. Voltage and current waves
10. Characteristic line resistance
11. Reflection at the end of the line
12. Reflection factor
13. Voltage trends at the ends of a line
14. Table method
15. Harmonic transmission lines
16. Linear parameters
17. Line equation (telegrapher's equation)
18. Solving for negligible losses (radio electrician's equation)
19. General harmonic solution
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. Reflectance 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 To mechanical engineering

            1.3 Wave-corpuscle duality

2. Schrödinger equation for the free particle

            2.1 Schrödinger 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. Diffusion by a potential in space

            3.1 Finite potential well

            3.2 Potential walk

            3.3 Potential barrier