Finding phase difference between two sinusoids

Click For Summary

Discussion Overview

The discussion revolves around finding the phase difference between two sinusoids with different frequencies and amplitudes. Participants explore the implications of differing frequencies on the concept of phase difference, as well as the relevance of amplitude in this context.

Discussion Character

  • Homework-related
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that the phase difference could simply be pi/3, questioning whether the differing amplitudes matter.
  • Another participant expresses uncertainty about the simplicity of the phase difference calculation and asks if amplitude differences have any impact.
  • Some participants argue that the phase of the second sinusoid is not zero but rather pi, and they question the validity of discussing phase difference when the frequencies are not the same.
  • It is proposed that phase differences only make sense for sinusoids of identical frequencies, with a reference point necessary for meaningful comparisons.
  • A participant elaborates on the nature of phase as a relative measurement, emphasizing that comparing phase angles of different frequencies lacks relevance.
  • One participant illustrates the issue with a metaphor about positional differences between two people on different buses, highlighting the complications of comparing phase when frequencies differ.
  • Another participant suggests that if a phase difference must be established, it would need to be expressed in a time-dependent manner, which complicates the concept further.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of calculating phase difference between sinusoids of different frequencies. While some suggest that it can be done, others argue that it does not make sense and that a reference point is necessary for meaningful comparisons.

Contextual Notes

Participants note that the phase difference calculation is contingent upon the frequencies being identical, and that without a common reference point, the phase information may not be useful. The discussion highlights the complexities involved in comparing sinusoids of differing frequencies and amplitudes.

neshepard
Messages
67
Reaction score
0

Homework Statement


I have a graph of two sinusoids which I need to find the frequency of and phase difference between the two. I have the frequency easily enough, I hope, and I found what I believe is the actual formula for each wave. But I have no clue as to finding the difference.

Homework Equations


Frequency
V1(t) = 250Hz (period of 4mS)
V2(t)=333.33Hz (period of 3mS)

I have the following formulas for the waves.
V1(t)=4Vcos(2pi250t + pi/3)
V2(t)=-3Vcos(2pi333.33t)

The Attempt at a Solution


From here, the textbook is blank. Is the difference just simply pi/3? And does it matter that the waves have different peak heights? Any and all help is appreciated.
 

Attachments

  • 1.jpg
    1.jpg
    44.8 KB · Views: 951
Last edited:
Physics news on Phys.org
neshepard said:

The Attempt at a Solution


From here, the textbook is blank. Is the difference just simply pi/3? And does it matter that the waves have different peak heights? Any and all help is appreciated.

\theta_{difference}=\theta_{1}-\theta_{2}
 
Really, that easy? Do I feel dumb or what? Thanks! Do you know if the wave peak amplitude differences make any difference?
 
neshepard said:
Really, that easy? Do I feel dumb or what? Thanks! Do you know if the wave peak amplitude differences make any difference?

What do you think?
 
I guess I would have to say no. Provided the waves are out of phase by the same θ at all times, then they only differ in the θ.
 
neshepard said:
I guess I would have to say no. Provided the waves are out of phase by the same θ at all times, then they only differ in the θ.

:smile:
 
Thanks
 
Two problems.

1. The phase of the v2 (as written in the OP) is not 0, it is \pi.

2. I don't think it even makes sense to talk of the phase difference when the frequencies differ.
 
Last edited:
Indeed, it does not make sense to speak of phase difference unless the frequencies are identical. (Except maybe when talking about PLL's and instantaneous phase errors, but that's another topic for another day.)
 
  • #10
Problem is, that's the homework assignment. Mine is not to question why, ...
 
  • #11
The only way you could bring phase into it is, maybe at t=0 you could specify the phase of each relative to a sinewave of the same frequency. This would indicate the initial phase angle of that sinusoid at t=0, and may be as essential as specifying amplitude.

But it is not possible to compare relative phase angles of waves at different frequencies.
 
  • #12
The problem is that phase is a relative measurement. It is the excess radian angle measured with respect to some rotating angular reference. With v1 for example, the phase is \pi/3 relative to a cosine angular reference of 500 \pi t. A phase angle like this only really contains useful information if the reference is known, which implies a particular t=0. This is not possible in all situations.

For the case of two sinusoids of the same frequency however, the notion of phase is more useful, because in taking the difference of the total angles, the two reference phases (2 pi f t) cancel out (by subtraction) leaving a phase difference which is independent of the exact time origin. This is by far the most useful case for the notion of a phase angle.

For the case of sinusoids of different frequency however the situation is much worse. Not only is a naive calculation of phase difference (as per propose early in this thread) relative to a particular t=0 but each of the phase angles are relative to two completely different speed rotating angular references!

It's like if I was traveling on a bus on a Nth-Sth running highway and my N-S position relative to the front of the bus was -2.4m. My friend is also on a bus on the same highway and his N-S position relative to the front of the bus is -3.6m. So I conclude that the "positional difference" between me and my friend is 1.2m. The only problem is that he is on a different bus traveling at a different speed. How much relevance does my "positional difference" calculation hold?

If you must have a phase difference between the two then it would have to be something like 166.67 \pi t + \frac{2 \pi}{3}, which is neither constant nor independent of the time origin.
 
Last edited:

Similar threads

Phase difference RLC circuit
  • · Replies 5 ·
Replies
5
Views
3K
How to Determine Phase Difference Between Two Sinusoidal Signals
  • · Replies 10 ·
Replies
10
Views
2K
Three phase star connection with different offset
  • · Replies 2 ·
Replies
2
Views
2K
Difference between phase angles
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Superheterodyne Receiver with Phase Sensitive Detection Question
  • · Replies 3 ·
Replies
3
Views
2K
Engineering Sinusoidal steady state analysis using Laplace transform
  • · Replies 3 ·
Replies
3
Views
3K
Find the phase difference between these two sine waves
  • · Replies 21 ·
Replies
21
Views
1K
Calculate the phase angle between two sinusoids
  • · Replies 2 ·
Replies
2
Views
4K
Engineering Current phase angle difference (AC circuit)
  • · Replies 33 ·
2
Replies
33
Views
4K
Undergrad How Can Two Waves with Different Amplitudes Be in Phase?
  • · Replies 5 ·
Replies
5
Views
2K