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How to apply the leading-lagging terminology for standing wave loops? Suppose we have standing wave:

$$y=10\sin(\frac{4\pi x}{5})\sin(10\pi t)$$

Then do we say that first loop (from $x=0$) is lagging by "$π$" radians or leading by "$π$" radians w.r.t the second loop?

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There is no right or wrong as to which motion is leading/lagging the adjacent loop. There is a $\pi $ phase difference and you can choose whatever term (lead/lag) you like in whatever order of mentioning the loops you like.

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  • $\begingroup$ So there isn't any convention as such? $\endgroup$
    – user102705
    Mar 17 '17 at 14:40
  • $\begingroup$ They are mathematically identical for standing waves. $\endgroup$
    – Yashas
    Mar 17 '17 at 14:41
  • $\begingroup$ @YashasSamaga Indeed they are. I wanted to ensure if there is any convention to be followed while using the leading-lagging terminology in standing waves. $\endgroup$
    – user102705
    Mar 17 '17 at 14:42
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    $\begingroup$ Not in this example. Usually you can say that motion A does something and then later motion B does whatever motion A was doing. So for a right travelling wave there is a direction and particles to the right lag behind those to the left. There is no such reference point here. $\endgroup$
    – Farcher
    Mar 17 '17 at 14:45
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If you take a picture of the standing wave at some instant, you would see something similar to the image shown below.

enter image description here

The particles between the first and the second node are moving downwards (or upwards). The particles between the second and the third node are moving upwards (or downwards). The particles of the two sections are off by a phase difference of $\pi$.

Adjacent loops are always out of phase by $\pi$ and only $\pi$.

If your question was which term to use, i.e: 'leading' or 'lagging', you can use any term as they are mathematically equivalent because the phase difference is $\pi$.

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  • $\begingroup$ This does not answer my question. $\endgroup$
    – user102705
    Mar 17 '17 at 14:39
  • $\begingroup$ I was wondering if you were actually the difference between lagging and leading phase difference in the case of standing waves. If that was the question, then which term you use does not matter because they mean the same as the difference is $\pi$. $\endgroup$
    – Yashas
    Mar 17 '17 at 14:41

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