Classical Wave Mechanics

Classical wave mechanics describes the behavior of waves in physical systems, from sound waves in air to light waves in space. These phenomena were well understood before the advent of quantum mechanics.

Wave Equation

The classical wave equation in one dimension is:

∂2y∂t2=v2∂2y∂x2\frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2}

where:

  • y is the displacement
  • t is time
  • x is position
  • v is wave velocity

Wave Properties

Wave Speed

v=fλv = f\lambda

where f is frequency and λ is wavelength

Standing Waves

y(x,t)=Asin⁡(kx)cos⁡(ωt)y(x,t) = A\sin(kx)\cos(\omega t)

where:

  • A is amplitude
  • k is wave number
  • ω is angular frequency

Wave Phenomena

  • Interference and Superposition
  • Diffraction and Huygen's Principle
  • Reflection and Refraction
  • Doppler Effect

Applications

  • Sound waves and acoustics
  • Water waves
  • Electromagnetic waves
  • Seismic waves