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How do I determine the phase difference between particles A and C? Particles A oscillates up and down, but particles C remains unchanged. So it seems that the phase difference varies between A and C dependent on the position of A. Is this correct? I posted a question like this recently however I mistakenly asked for the phase difference between A and B. I am looking for the phase difference between A and C.

EDIT: Is the answer of a constant 90 degrees phase difference correct? I cannot see how this is the case.

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    $\begingroup$ Does this answer your question? Phase difference with standing waves and, assuming that it is a standing wave, there is an explicit statement that the phase difference between $A$ and $B$ is zero. $\endgroup$
    – Farcher
    Aug 9, 2023 at 7:23

2 Answers 2

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A standing wave is the superposition of two waves of the same frequency and amplitude traveling in opposite directions. They are characterized by nodes, where there is no motion, and antinodes, where the motion is at a maximum.

A standing wave takes the form: y(x,t)= 2 A sin(kx) cos(ωt)

Where:

y(x,t) is the displacement of the string as a function of position and time

A is the amplitude of the original traveling waves. k is the wave number, which equals 2 π/λ λ being the wavelength. ω is the angular frequency,

All the nodes are fixed and do not undulate. Point C is such a point. The phase difference between each nearest neighbor node is Pi. You can use this measure to compute the phase difference for any other 2 points. So, A-C would be Pi.

To understand why, consider the basic equation for a standing wave. At a node y(x,t)=0 for all values of t This means that sin(kx)=0. The sine function is zero at 0, π, 2π, and so on...

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What you have plotted is a standing wave. The amplitude of the wave varies with time, but the phase difference is constant at pi/2 for the A and C. D Sin(omega t) Sin(kx) is a typical form of standing wave. There are other forms too. D is constant. Phase differnce is position dependent you are correct.

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  • $\begingroup$ Particle $C$ is not oscillating and so is at its equilibrium position. You could say that relative to particle $C$ the phase of particle $A$ varies between $0^\circ$ and $360^\circ$. At the instant shown for particle $A$ and assuming it is at a maximum displacement then the phase difference is $\pi/2$. relative when it was at the equilibrium position. $\endgroup$
    – Farcher
    Aug 9, 2023 at 7:31
  • $\begingroup$ @SAkhan. You say that phase difference is positional dependent. So how can there be a constant phase difference between A and C if the amplitude or position is changing? $\endgroup$ Aug 9, 2023 at 18:58
  • $\begingroup$ The position dependence means the position of the particle as its projection on the x axis that doesn't change with time. I have made the correction the phase difference is pi/2 not pi/4. $\endgroup$
    – SAKhan
    Aug 10, 2023 at 0:21
  • $\begingroup$ See kx term k=2 pi/lambda $\endgroup$
    – SAKhan
    Aug 10, 2023 at 0:30

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