I'm convinced that water waves for example:
are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?
Answer
Each point is moving according to:
x(t)=x0+ae−y0/lcos(kx0+ωt)
y(t)=y0+ae−y0/lsin(kx0+ωt)
With x0,y0 -- "motion centre" for each particle, a -- the amplitude, l -- decay length with depth.
So you have exact "circular" superposition of longitudinal and transverse waves.
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