A possible solution for the equation:

÷{∂}{∂t}(÷{∂}{∂t}(X))=c²⋅∆(X)

... which is the same as...

(∆-÷{1}{c²}⋅÷{∂}{∂t}÷{∂}{∂t})X=0

... which is the same as...

⧠X=0

... is:

X(r⃗,t):=X_0⋅\exp(i⋅(ω⋅t-k⃗∙r⃗))

...where...

|k|=÷{2⋅π}{λ}
ω=2⋅π⋅f
f⋅λ=c

Another valid solution is:

X(r⃗,t):=X_0⋅\cos(ω⋅t-k⃗∙r⃗+α)