A wave packet with angular frequency $ω_{0}$ is propagating in dispersive medium with phase velocity of $1.5 \times 10^{3}$ m/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?

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$0.25 \times 10^{3} m / s$

$1.0 \times 10^{3} m / s$

$0.75 \times 10^{3} m / s$

$0.6 \times 10^{3} m / s$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Velocity of wave or phase velocity; $v_{p} = \frac{ω}{k}$

$\Rightarrow \frac{{dv}_{p}}{v_{p}} = \frac{dω}{ω} - \frac{dk}{k}$

$\frac{dk}{k} = \frac{dω}{ω} - \frac{{dv}_{p}}{v_{p}} = 2 % - (- 3 %) = 5 %$

Group velocity is given by,

$v_{g} = \frac{dω}{dk} = v_{p} (\frac{\frac{dω}{ω}}{\frac{dk}{k}}) = 1.5 \times 10^{3} (\frac{2}{5})$

= $0.6 \times 10^{3} m / s$

Watch 3-min video & get full concept clarity