# 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.