A wave packet with angular frequency `omega_0` is propagating in dispersive medium with phase velocity of `1.5xx10^3m//s`. When the frequency is increased by `2%`, the phase velocity is found to decrease by `3%` what is the group velocity of the wave packet?

Options

A. `0.75xx10^3m//s`
B. `1.0xx10^3(m)/(s)`
C. `0.25xx10^3m//s`
D. `0.6xx10^3m//s`

Answer

D

Explanation

Velocity of ware or phase velocity `v_p=(omega)/(k)`
`implies(dv_p)/(v_p)=(domega)/(omega)-(dk)/(k)`
`(dk)/(k)=(domega)/(omega)-(dv_p)/(v_p)=2%-(-3%)=5%`
Group velocity is given by
`v_g=(domega)/(dk)=v_p((domega//omega)/(dk//k))=1.5xx10^3((2)/(5))`
`=0.6xx10^3m//s`