PX154 - H1 - fixed and free ends

[YF 15.6]

fixed end

• wave is reflected when it reaches the ends

• we are considering that the wave energy is reflected at the ends

• eg:

  • boundary condition: an end fixed at $y=0$
  • reflected wave is inverted
  • boundary condition: $y_{total}(x_0)=0$

free ends

• eg:
  • organ pipe - wave reflected at the open end
  • sound waves echoing off a wall
  • light reflecting off a mirror
  • QM treatment of particles in a potential well
• eg:
  • frictionless ring, free to move along $y$
  • consider the ring to be massless
  • comparing it with the equation for a ring with mass, $m$, from the waves worksheet, we find the boundary condition to be:
  $${\left(\frac{\partial y}{\partial x}\right)}_{x_0}=0$$