The phase $Φ$ of wave is defined as $kx-wt$. It should be the case that all observers moving relative to each other in the non relativistic case will agree on this.
So given the transforms $x'=x-vt$ and $t=t'$,
$Φ'=kx'-wt'$
$=k(x-vt)-wt$
$=kx-wt-kvt$
Seeing as this is wrong, how does one properly show that the phase of a wave is Galilean invariant.