Question

Why superposition principle not true for large amplitude?

Answer 1

If a wave f(x,t)f(x,t) is something that satisfies the wave equation Lf=0Lf=0where LL is the differential operator ∂2t−c2∇2∂t2−c2∇2 then, because LL is linear, any linear combination λf+μgλf+μg of solutions ff and gg is again a solution: L(λf+μg)=λLf+μLg=0L(λf+μg)=λLf+μLg=0.

In general, there might be things that propagate (not exactly waves, but since the question is for waves of any kind) determined by other differential equations. If the equation is of the form Lf=0Lf=0 with LLa linear operator, the same argument applies and the superposition principle holds.


THIS ALL I LEARNED...