To form a standing wave, two coherent waves must travel in opposite direction. But is it it necessary for them to have the same amplitude and no phase angle difference?

  • 3
    $\begingroup$ You can check it yourself. Just write down two waves with different amplitude/phase and add them $\endgroup$ Apr 1 '16 at 18:37
  • $\begingroup$ One can plot is it as well, www.desmos.com $\endgroup$
    – Kashmiri
    Jan 30 '21 at 17:11

The fact that they are coherent means they have a constant phase difference. And from a constant phase difference it follows that their interference pattern will be stationary.

However, unless they have the same amplitude, the nodes of the "standing wave" will not be completely zero. Instead, you can think of the larger one as the sum of two waves. If we call the wave traveling to the right A, and the one traveling to the left B, then we can write $A=A_1 + A_2$ where $A_1$ has the same amplitude as $B$. Then $A_1$ and $B$ will form a standing wave pattern, and superposed on that pattern is the wave $A_2$. When $A=A_1$, $A_2=0$ and you have a perfect standing wave.

  • $\begingroup$ How can I help clear that confusion for you? $\endgroup$
    – Floris
    Apr 2 '16 at 12:48
  • $\begingroup$ First of all thank you a lot, but i still i have some confusion:-a) Suppose they are not coherent and they have a phase difference, then will a standing wave be formed. B) You mentioned that they won't form perfect standing waves if their amplitudes are not same , so basically standing waves is possible even if their amplitudes are not same.Again, thank you a lot. $\endgroup$ Apr 2 '16 at 12:57
  • $\begingroup$ Well if waves travel in opposite directions their phase difference depends on the point where you measure it. As long as they have the same frequency there will be a stationary point where their phase difference is zero $\endgroup$
    – Floris
    Apr 2 '16 at 13:01
  • $\begingroup$ As for the second point - if they are not of the same amplitude they will not form a "perfect" standing wave (with a zero node) but a "partial" one. In RF engineering partial reflection (of signal into an antenna for example) is very important and it is measured by looking at the "standing wave ratio" - the ratio of amplitudes at the antinode vs the node. This is one when there is no reflection and infinite for perfect reflection (equal amplitude in both directions) $\endgroup$
    – Floris
    Apr 2 '16 at 13:05
  • $\begingroup$ So basically, to form a standing wave , two waves must have the same frequency and they must be travelling in opposite direction? $\endgroup$ Apr 2 '16 at 13:06

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