A wave packet with angular frequency ω0 is propagating in dispersive medium with phase velocity of 1.5× 103 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?
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a
0.75 × 103 m/s
b
1.0 × 103 m/s
c
0.25×103 m/s
d
0.6×103 m/s
answer is D.
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Detailed Solution
Velocity of wave or phase velocity; vp = ωk⇒ dvpvp = dωω-dkkdkk = dωω-dvpvp = 2%-(-3%) = 5%Group velocity is given by,vg = dωdk = vp(dωωdkk) = 1.5×103(25) = 0.6×103 m/s