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Wave Packets, Group velocity, and Phase velocity [duplicate]

Mathematically, you find that the wave function of a particle $\Psi (x,t)$ moves with the same velocity as the velocity of the particle ($v_{particle} = v_{group}$). Is there a reason why the ...
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What does the velocity of a wave mean?

I know that the velocity of a wave is given by $v=\lambda f$ but what does this velocity represent in the physical sense. For instance, if I am told a car moves at a velocity of 5 $m/s$ I know that ...
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Group Velocity and Phase Velocity of Matter Wave?

In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
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How do you find the velocity function of a mechanical wave?

With the form $y(x,t)=A\sin(kx-\omega t+\phi_0)$, there are two variables, How do I find the velocity? I don't know I can apply derivative with two variables.