Quick calculation for a transverse wave on a string.
Let T= tension on the string.
Let mu= mass per unit length of the string.
Let the string lie along the x axis, and
let the displacement of the wave be in the y direction.
The energy density of the wave is then:
0.5*mu*(dy/dt)^2 + 0.5*T*(dy/dx)^2.
The current of energy (flux) is:
-T*(dy/dt)*(dy/dx).
Dividing this by the speed of the wave gives:
-sqrt(mu*T)*(dy/dt)*(dx/dt)
which would be a momentum flux for the wave.
(sqrt is the square root function)