GROUP VELOCITY:-

When a number of waves of slightly different wavelengths and velocities travel together in a medium the observed velocity of this group of waves is called the Group velocity. Such a group of waves is called a wave packet.

PHASE VELOCITY:-

The velocity with which a wave travels through a medium is known as phase velocity or wave velocity. RELATION BETWEEN PHASE AND GROUP VELOCITY.

Consider a particle of rest mass m_o moving with a velocity v, which is very large and comparable to c with v<c ,="" its="" mass="" is="" given="" by="" the="" relativistic="" formula.<="" p="">

$ m=m_o/(√1-(v^2/c^2 ))$

$ ω=2πϑ……..$( ω = angular frequency )

$ =2π(E/h)=2π(mc^2/h)$

$ And k= 2π/λ= 2pπ/h= 2π/h(mv) Wave velocity is the phase velocity given as $ V_p= ω/k=c^2/v$ $ V_p = dω/dk$ $ V_g= (dω⁄dv)/(dk⁄dv)$ $ V_g=V$ This shows that a matter particles in motion is equivalent to a packet moving with group velocity $V_g $whereas the component waves moves with phase velocity$ V_p$. Hence the relation between phase velocity and group velocity is:- $∴V_p V_g= c^2$