Mechanical wave propagation

Propagation of a signal - Notion of wave

Propagation of sound in a solid: infinite chain of springs - transition to a continuous medium
One-dimensional d'Alembert equation in several areas of physics


Travelling wave - superposition of waves

General solution of the one-dimensional d'Alembert equation
Travelling wave in the case of one-dimensional linear non-dispersive propagation. Velocity, time delay
Sinusoidal travelling wave: phase shift, double spatial and temporal periodicity
Coupled variables. Impedance Reflection and transmission coefficients on a discontinuity
Interference between two mechanical waves of the same frequency
Notion of eigenmodes: situation where all degrees of freedom have a sinusoidal time evolution of the same frequency. Example of the horizontal motion of two masses suspended by massless linear springs
Generalization to several degrees of freedom (N degrees of freedom = N eigenmodes)
Eigenmodes of a string fixed at both ends or of a sound pipe
Spectral analysis


Sound waves in fluids

Equation of sound waves in the acoustic approximation
Energy aspects : volume density of sound energy, energy current density vector
Reflection and transmission of a progressive plane sound wave under normal incidence on an infinite plane interface between two fluids: reflection and transmission coefficients of velocities, overpressures and sound powers.


Dispersion - absorption

Examples of situations where propagation speed depends on wave pulsation
Phase velocity
Wave packet spreading - group velocity

Signal propagation - Notion of wave
Travelling wave - superposition of waves
Sound waves in fluids
Dispersion - absorption