Understanding Wave Phase: Definition and Equations

[foxjwill]

Homework Statement

What is the definition of the phase (not phase shift) at some time t of a wave? Specifically, for a wave oscillating according to the equation

$$x=A\sin(\omega t + \phi),$$

what is the the phase at some time $$t$$?

Homework Equations

The Attempt at a Solution

Our book says the phase is $$\omega t + \phi,$$ while http://en.wikipedia.org/wiki/Phase_%28waves%29" says that it can also be $$\omega t + \phi$$ modulo $$2\pi$$. Which is right?

 

[astrorob]

I suggest you reread the wikipedia definition (in this case), they mightn't be as different as you think.

On a side note, I would be wary of taking wikipedia for gospel. It is very useful, but mistakes can be common.

 

[foxjwill]

I suggest you reread the wikipedia definition (in this case), they mightn't be as different as you think.

I know that they're not that different, but the reason I'm asking is that I lost points on a quiz for using the modulo $$2\pi$$ value because my teacher chose to use the definition given by our book (which I had forgotten since this was a review quiz on material we covered last semester).

On a side note, I would be wary of taking wikipedia for gospel. It is very useful, but mistakes can be common.

Yes, but that's why I'm asking. I couldn't find very much about either definition of phase anywhere else, although I didn't take very much time to look.

 

[astrorob]

Well, as Wikipedia mentions, I think it's one of those things that isn't as clear cut as perhaps it should be.

Personally I'm with you since the $$\omega t + \phi,$$ and its corresponding modulo $$2\pi$$ value will both yield the same value under trigonometric function.

However, I can see the flip side of the coin. If the phase is defined as the number between the brackets, then strictly speaking that number is not the same as its modulo $$2\pi$$ value.

Sorry I can't be of more conclusive help!
Rob.