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For progressive waves we define phase difference as difference in phase angle between two points. However for standing waves, the phase difference becomes something else. We say two points are in phase when they travel in the same direction and with the same amplitude. So why have the definitions changed here?

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We say two points are in phase when they travel in the same direction and with the same amplitude.

The amplitude does not have to be the same.

Think of phase in terms of a two repetitive motions each of period $T$.

Being in phase means that the two motions are at the same point in the repetitive cycle at a given time eg the motions reach a maximum displacement at the same time.

If the time difference between one motion reaching a maximum and the other motion reaching a maximum is $t$ then the phase angle between the two motions is $\frac tT\,2\pi$ radians or $\frac tT\,360$ degrees.

In a standing wave all motions between two adjacent nodes are in phase, and the motions either side of a node are $\pi$ radians or $180^\circ$ out of phase.

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  • $\begingroup$ How would you define phase difference? $\endgroup$ Aug 3, 2023 at 9:26
  • $\begingroup$ Phase angle is a way of describing phase difference in terms of angles. $\endgroup$
    – Farcher
    Aug 3, 2023 at 10:17

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