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Why does superposition principle fail at high amplitudes. Please answer with respect to transverse waves. If possible, plane progressive transverse waves at best.

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    $\begingroup$ Non-linearity ... $\endgroup$ – John Rennie Apr 16 '16 at 16:10
  • $\begingroup$ Please see our guide on writing good titles. $\endgroup$ – user10851 Apr 16 '16 at 18:32
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For a general answer concerning these types of systems, we can take the simple gravity pendulum as a representative example. The equation of motion is generally non-linear, but can be approximated to be linear at small angles (small amplitudes). See also the small angle approximation section in the linked wikipedia article.

For progressive waves you will have many coupled such oscillators, which will exhibit wave motion. The non-linearity still comes from this type of equation of motion. The exact equation will depend on your system, but most of real systems are only linear within some approximation (if at all). Even electromagnetic waves in the vacuum above a certain energy limit...

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