But for certain cases, such as wave propagation in lossy deielectric, in transmission lines or in waveguides, etc. the phase constant is not a linear function of frequency 
and waves of different frequencies will proopagate with different phase velocities. The transmission bearing signals used for communication consists of a band of frequencies. The medium where, the phase velocity is dependant on frequency, the componet frequencies of the wave travel with different phase velocities causing distortion in the signal wave shape. Such signal distortion caused by the dependance of the phase velocity with frequency is called dispersion.
If the information bearing signal is narrow band i.e. has a small spread of frequencies around a high carrier frequency, a group velocity term is defined to describe the velocity at which such narrow band signal propagates. The same is illustrated below.
Let us consider a narrow band signal consisting of two traveling waves of equal amplitude, having frequencies 
and 
around a centre frequency 
such that 
such a signal can be described as
where 
and 
are the phase constants corresponding to the frequencies and .