G.Y
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Why is total cancellation of waves rarely achieved in practice?

Is it because 2 waves are unlikely to have exactly the same amplitude and wavelength?
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uberteknik
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(Original post by G.Y)
Why is total cancellation of waves rarely achieved in practice?

Is it because 2 waves are unlikely to have exactly the same amplitude and wavelength?
In essence, yes.

Think about the words 'in-practice':

What types of wave are their? What are the physical manifestations of a wave? i.e. ripples on a pond, sound in air, standing wave on a rope, electromagnetic propagation, symmetry etc.

Then think of things like pond depth, air density localised changes, uniformity, absorption, energy losses, eddy currents, reflection, scattering etc. and how waves are modified and interact in those environments.

These give rise to and contribute to (in greater or lesser degrees) amplitude differences, changes in velocity of propagation -hence wavelength- in the propagation medium, scattering, non-linearities, frequency shifting etc. etc.

In physics, the laws and mathematics are exact. The engineering, in reality, always modifies the models to account for physical imperfection.
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