How do i know what a function describe a wave?

[Darly]

Homework Statement

Show that the funtions y(x,t) and g(x,t) satisfy the differential equation of a wave unimensional. What function is a wave?

Homework Equations

y(x,t)=x² +v²t² ; d(x,t)= 2Acos(kx)cos(wt)

frac{d²y}{dt²}=2v²

frac{d²y}{dx²}=2

The Attempt at a Solution

frac{d²y}{dt²}=2v²

frac{d²y}{dx²}=2

frac{d²g}{dt²}= -2Aw²cos(kx)cos(wt)
frac{d²g}{dx²}= -2Ak²cos(kx)cos(wt)

Comparing the two functions with the wave equations with y(x,t) and g(x,t) satisfy the equation differential of wave, if all is correct, can i say that the functions are waves. ?

 

[blue_leaf77]

if all is correct, can i say that the functions are waves. ?

Yes.

 

[PietKuip]

A constant wave can be written as a function of x-vt.