Wave equation derivation Why is the angle assumed to be small?

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SUMMARY

The discussion centers on the derivation of the wave equation, specifically addressing the assumption that the angle theta, which the string segment makes with the horizontal, is small. This assumption is crucial because it ensures that the wave equation remains linear and accurate for small-amplitude oscillations. For larger amplitudes, the wave behavior becomes non-linear, leading to inaccuracies in the simple wave equation. The key takeaway is that the small angle approximation is valid only when the amplitude of oscillation is minimal.

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McLaren Rulez
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http://www.math.ubc.ca/~feldman/apps/wave.pdf is the link from where I understood how to derive the wave equation. But why is theta assumed to be small? As I understand it, theta is the angle that the string segement we're considering makes with the horizontal. Even a simple sine wave seems to form pretty reasonable angles with the horizontal. So what's my misconception here? Thank you
 
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Depends on the amplitude of the sine wave. The simple wave equation won't be quite correct for large-amplitude oscillations, which will make the system non-linear (waves won't pass through each other unscathed as they do with the simple wave equation).
 
So essentially, the assumption is that the amplitude of oscillation is small. Thank you for clearing that up.
 

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