Understanding Wave Phase: Definition and Equations

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Homework Help Overview

The discussion revolves around the definition of the phase of a wave, specifically in the context of the wave equation x=A\sin(\omega t + \phi). Participants are exploring the nuances between different definitions of phase, particularly the distinction between using the phase as \omega t + \phi and considering it modulo 2\pi.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the validity of different definitions of phase as presented in their textbook and Wikipedia. They are discussing the implications of using modulo 2\pi and how it relates to grading and understanding in their coursework.

Discussion Status

The discussion is ongoing, with participants sharing their perspectives on the definitions of phase. Some have provided guidance on the potential similarities between the definitions, while others express uncertainty about the clarity of the concept. There is no explicit consensus yet, but the dialogue is productive.

Contextual Notes

Participants mention previous experiences with quizzes that impacted their understanding of the definitions, indicating that educational context and instructor preferences may influence their interpretations of phase.

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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

[tex]x=A\sin(\omega t + \phi),[/tex]

what is the the phase at some time [tex]t[/tex]?


Homework Equations





The Attempt at a Solution


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

astrorob said:
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.
 
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 [tex]\omega t + \phi,[/tex] and its corresponding modulo [tex]2\pi[/tex] 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 [tex]2\pi[/tex] value.

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

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