PHYS20171 MATHEMATICS OF WAVES AND FIELDS

Wave Figures

Here are some figures which illusrate some of the concepts associated with waves.

Velocity

The red dot in these two figures shows a point in the wave moving with the phase velocity. The green dot in the second figure shows a fixed location in the wave. This moves with the group velocity.

• Phase velocity
• Group velocity

Wave packets

Notice how the waves making up the non-dispersive packet maintain their relative positions in the wave packet, whereas in the dispersive packet the individual peaks move through the packet.

• Non-dispersive wave packet
  
• Dispersive wave packet
  
• Dispersive wave packet - Real part of the solution to Schrodinger's equation in free space.
  

(All the graphics shown above are from various pages on Wikipedia. The specific links can be found in the Waves section of the Web Resources page for this course.)