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Phase velocity is the velocity of the high-frequency wave inside the envelope. While group velocity is the velocity of the low-frequency wave that makes the envelope. If these velocities are different, how can the high-frequency wave remains fixed within the low-frequency wave envelope? In a word, I am having trouble in visualizing the wave packet where the wave inside the envelope has one speed & the envelope has other speed. Can I be helped?

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    $\begingroup$ Wikipedia has some nice visualisations. $\endgroup$ – Harry Wilson Mar 6 '15 at 10:42
  • $\begingroup$ @Harry Wilson: Thanks, sir. It was a great help, indeed. Actually I am using a very old version of Opera in my mobile that doesn't support animation. But through UC, on your advice, I went to the wiki page & it made me clear! $\endgroup$ – user36790 Mar 6 '15 at 17:58
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I have plotted curves where you could see it(it is not very clear I am afraid but the explanation is inside).

enter image description here

The first graph shows 2 waves with slightly different frequencies going at the same speed. The green curve is the sum of the 2 sinusoidal wave and represents a beat that goes at the same speed as the 2 waves.

On the second graph, the high frequency sinus(blue curve) goes slower than the low frequency(red). You can ideed see it because the maximums of the blue curves do not appear at the same position as in the first graph whereas they do for the red one. We still have a beat for the sum but this time we can see that it goes slower than the beat in the first graph. The happens because when the 2 sinus add in the second graph, their maximum is not at the same place as in the first graph.

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  • $\begingroup$ I will try to make something even more easy to visualize if it is still not clear enough. $\endgroup$ – Ronan Tarik Drevon Mar 6 '15 at 15:19
  • $\begingroup$ +1. Thanks not only for your answer but also for the modest attitude you offered, sir. I'll ask for your help if required. $\endgroup$ – user36790 Mar 6 '15 at 18:01

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