Group
 Velocity
 •The group velocity of a wave is the velocity with which
 the overall shape of the wave's
 amplitudes (i.e. envelope) propagates through space.
•Two horizontally propagating waves of equal amplitude
 but slightly different wavelengths
 with wave numbers and frequencies differing by 2δk and 2δν, respectively. The total disturbance is thus:
 
  
  
  
  
  
  
  
  
 
  
  
 
  
  
 
  
 
  
 
  
  
  
 
 
 
 
 
 high-frequency carrier wave
  
 
 
 
 
 
 low-frequency amplitude
 modulation
  
 
 
 
 
 
 travels at the speed of δν/δk è
 group velocity
  
 
  
 