Phases of SHM & Wave Motion: Are They Equal?

[sadhu]

My teacher told me that in SHM and wave motion phase refers to the argument in the corresponding function. then she said that if there is a difference of 2pi in the arguments then the phases are equal (sin ,cos function)

but isn't it wrong , i know that their effect in terms of velocity , acc. ,displacement will be same but I can't get how they are equal if their is a difference of 2 pi between them??

 

[Doc Al]

What's the difference between \sin (\theta) and \sin (\theta + 2 \pi)?

 

[sadhu]

they are same , but they are not the phases the phase is the term inside which is not same

 

[Doc Al]

Not sure what you mean. If two sinusoids are "out of phase" by 2 \pi, then they are actually in phase. A phase difference of 2 \pi is the same as no phase difference at all.

 

[sadhu]

I still think that it is counter intuitive, how can two quantities have a difference between them and then be equal , how can it be possible mathematically .

 

[jtbell]

I think the problem here is simply subtle differences in terminology. People use the word "phase" to mean two different (although related) things. Sometimes it means "which point in a single complete cycle of the sine or cosine" and in that case 0, 2\pi, 4\pi, ... are all the same phase because they are all at the beginning of a cycle.

Sometimes it means "the argument of the sine or cosine" and in that case 0, 2\pi, 4\pi, ... are different phases. This difference can be significant when you consider oscillations over more than one cycle: phase = 0 is the beginning of the first cycle, phase = 2\pi is the beginning of the second cycle, etc.

I personally think the second meaning is more precise. I prefer to say that two waves with phases of 0 and 2\pi are "in phase," not that they have the "same phase."

 

[Doc Al]

Good clarification, jtbell. I like it!

 

[sadhu]

Thanks for your clarification!