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I am confused. Usually, the wavelength is the x-distance between the tops of two consecutive waves. Here is the graph.

There is only 0.1 m between 2 crests. But the answer counts the wavelength as 0.2 m

enter image description here

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This happens because you are looking into a cosine squared, and not a regular cosine. The squared version will make the negative part positive, creating another crest where would be actually the minimum of the regular cosine. Therefore, in this case you must consider the second crest, providing the required answer.

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This is puzzling. But use the identity $$\cos^2(\theta)=\frac{\cos(2\theta)+1}{2}.$$ The period of $\cos(2\theta)$ is $\pi$, so the period of $\cos^2(\theta)$ is also $\pi.$ I think I disagree with the answer in your post. The period is $0.1$.

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  • $\begingroup$ Cos(x) is used for the wave speed. This is the power graph, where the speed got squared. $\endgroup$ – LetzerWille May 30 at 23:47
  • $\begingroup$ Yes, there should be more context involved on the question. Still, we should note that the "oscillations" in your consideration would be about the value of $1/2$, and not about zero. Subtle, indeed. $\endgroup$ – Bruno Anghinoni May 30 at 23:49
  • $\begingroup$ The "oscillations" in the power graph are about the value $R_s/2$. $\endgroup$ – user52817 May 31 at 0:10

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