# [Q]Do you know about exact form of Group velocity and meaning of Group Delay?

#### good_phy

Hi, It is long time to come here sine i graduate University.

Anyway, My question is whether exact form of Group velocity is $$\frac{dw}{dk}$$

or $$\frac{dw}{dk}|_{\bar{k}}$$

I want to know whether Group velocity is independent of K, propagation number

Becasue Group velocity is 'proper' speed of generally complex wave in comparision with

phase velocity So These exists only one Group velocity of certain wave which should not be

dependent of any K

Second Question is what does Group delay means? I have to drive Formula of Group delay

,$$\frac{d\varphi }{dw}$$ but i don't know what does it means.

Please Solve my question.

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#### jtbell

Mentor
Hi, It is long time to come here sine i graduate University.
Anyway, My question is whether exact form of Group velocity is

$$\frac{dw}{dk}$$

or

$$\frac{dw}{dk}|_{\bar{k}}$$

I want to know whether Group velocity is independent of K, propagation number
If $\omega$ is a linear function of k, then $d\omega/dk$ is a constant and the group velocity is well-defined.

If $\omega$ is not a linear function of k, then $d\omega/dk$ varies with k and one cannot speak of "the" group velocity, strictly speaking. Nevertheless, if a wave packet includes only a small range of k's, one can speak approximately of a group velocity by evaluating $d\omega/dk$ at $\bar k$, for a certain period of time. After a "long" period of time, the wave packet "falls apart."

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