Are phases with a 2π difference truly equal in SHM and waves?

[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!