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A sinusoidal wave is propagating along a stretched string that lies along x-axis. The wave is moving in +x-direction. Figure shows the graph of transverse displacement of particles of the string at x = 0 and x =4 cm as a function of time. The particles at x = 0 and x = 4 cm are within one wavelength of each other

I want to find the phase difference between particles at x=0 and x=4, and I think the phase difference should be either 7π/6 or 5π/6 ,how can we determine which of these is the correct phase difference and with what reasoning?

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  • $\begingroup$ You should add why you think it is 5/6 or 7/6 pi. $\endgroup$
    – JEB
    Commented May 2 at 2:16

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Looking at the graph below, the phase angle is defined as, $\phi_1 = \dfrac {T1}{T}\cdot 2\pi$, or $\phi_2 = \dfrac {T2}{T}\cdot 2\pi$, and note that $\phi_1+\phi_2 = 2\pi$.

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The choice of which phase angle to use is often arbitrary.

So you could say that:

whatever happens at position $x=0$ (graph $A$) occurs later by a time $T1$ at position $x=4$ (graph $B$) or

whatever happens at position $x=0$ (graph $A$) occurs earlier by a time $T2$ at position $x=4$ (graph $B$).

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  • $\begingroup$ But different choices of Phase difference will then lead to different wavelengths , so how will we decide to which particular wavelength the graph refers to? $\endgroup$
    – Garv Chaudha
    Commented May 2 at 13:44
  • $\begingroup$ The assumption is that the speed, wavength and frequency of the wave on the string do not change. $\endgroup$
    – Farcher
    Commented May 2 at 14:34

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