I'm strugggling with what should be an easy question;

I have a 2D free-surface water wave with surface displacement as follows,

\eta = Acos(Kx - \omega t)

Now what happens when you superimpose another wave of the same amplitude, but with a frequency of \omega + \Delta\omega and wavenumber K + \Delta K?

I thought that you should get an amplitude-modulated wave, but I'm not sure how to show this...

Help anyone? Thanks in advance!