A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 × 1 0 3 m / s . When the frequency ω is increased by 2% , the phase velocity is found to decrease b

Question

A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 × 1 0 3 m / s . When the frequency ω is increased by 2% , the phase velocity is found to decrease by 3% . What is the group velocity of the wave packet?

TestHub · Accepted Answer

Phase velocity, v p ​ = k ω ​ ​ v p ​ d v p ​ ​ = ω d ω ​ − k d k ​ ∴ k d k ​ = ω d ω ​ − v p ​ d v p ​ ​ = 2% − ( − 3% ) = 5% ​ Group velocity, v g ​ = d k d ω ​ ​ d k d ω ​ = v p ​ ( d k / k d ω / ω ​ ) = 1.5 × 1 0 3 ( 5 2 ​ ) = 0.6 × 1 0 3 m / s ​

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