Frequency and phase relationship

1. Sep 10, 2009

likephysics

Frequency is the time derivative of phase? But how?
Can someone explain?

2. Sep 10, 2009

f95toli

No, it is not.
At least not if you use the normal meaning of "phase", in which case it is a parameter (usually a constant) which tells you the relative postion in time of two or more periodic waveforms

e.g. if you have

$\sin (2\pi ft+\theta)$)

then $\theta$ would be the phase. Note that it is only meaningfull to talk about phase when you are comparing waveforms; the "starting point" for a periodic function is arbitrary so there is no such thing as absolute phase.

3. Sep 10, 2009

waht

Group delay is a derivative of phase with respect to angular frequency:

$$\tau_g = -\frac{d\phi}{d\omega}$$

4. Sep 10, 2009

likephysics

Last edited by a moderator: Apr 24, 2017
5. Sep 10, 2009

f95toli

OK, now I understand where you got that from.
This is why I was refering to the "normal meaning of phase" above.

People (meaning EEs) who work with modulations schemes (in this case FM) have a tendency to refer to the argument of the sine function as "phase" ; i.e "the phase" in this case would be $\omega t+\theta$ and if you take the time derivative of this you obviously get $\omega$ (which also happens to be the angular frequency, not the frequency).

So -unless I am missing something- this is just another case of confusion due to differences between EE and physics terminology.
The "definition" of phase I wrote above is certainly what you would find in a physics book.