My lecturer said that a standing wave is formed when two waves that travel in the opposite have the same frequency.(adsbygoogle = window.adsbygoogle || []).push({});

He said that if the waves are y_{1}and y_{2}, then the resulting wave y can be given as the sum:

y = y_{1}+ y_{2}.

y = Asin([tex]\omega[/tex]t - kx) + Asin([tex]\omega[/tex]t + kx). (1)

Where the plus and minus kx denotes their direction.

However, when (with a bit of trigonometric identity work) equation (1) is simplified it gives:

y = 2Asin([tex]\omega[/tex]t)cos(kx).

But how can this be? I mean, if x = 0, then the equation tells us that there is an antinode, which (for a string) isn't true.

I've seen the equation y = 2Acos([tex]\omega[/tex]t)sin(kx), which makes more sense when I consider a string for example.

To get to it you need the equation

y = Asin(kx - [tex]\omega[/tex]t) + Asin(kx + [tex]\omega[/tex]t) (2)

My question is, why would you use equation (2) and not equation (1)?

Thank you in advance for your help!

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# Standing Wave Equation

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