Question

Write relation between group and phase velocity in hindi

Answer 1

It depends on the dispersion relation.

Phase velocity is defined as vp=ωkvp=ωk

and group velocity is defined as vg=dωdkvg=dωdk

For electromagnetic waves ω=ckω=ck

Therefore, ωk=dωdk=cωk=dωdk=c

So, both group and phase velocities are same in this case.

Consider the dispersion relation for small waves on the surface of water body due to surface tension is ω(k)=σk3ρ−−−√ω(k)=σk3ρ

Here, you’ll find out vg=1.5vpvg=1.5vp(Just workout the math)