Useful Links about Fourier Analysis and Sinusoidal Wave Packets

 • A Visual Introduction to the Fourier Transform : If you are not as comfortable 
with Fourier Analysis as you would like, this 20-minute video is a magnificently 
intuitive introduction. Thank you to Ian Call for this recommendation!

 • When you superpose sinusoidal waves with wavelengths that are close to,
but not equal to, a central “carrier” wavelength, a wave packet is formed
that looks like the central carrier wave “modulated” by an envelope.  
The speed of the carrier is the phase velocity vph = ω/k of the packet while 
the speed of the modulating envelope is the group velocity vgr = dω/dk. 
These different speeds are succinctly illustrated in the following videos by 
meyavuz, where different relations between vph and vgr are demonstrated by 
playing with different dispersion relations ω(k).
    - Case 1 : vgr > vph
    - Case 2 : vgr = zero
    - Case 3 : vgr negative
    - Case 4 : vph = zero
    - Case 5 : vph > 0 and vgr < 0