A wave travels to the right on a string with constant tension and a mass density

A wave travels to the right on a string with constant tension τ and a mass density that slowly increases from ρ on the far left to ρ′ on the far right. The mass density changes slowly enough that its only effect is to change the speed with which the wave propagates. The waveform on the far left is A cos(kx−ωt) and on the far right is A′ cos(k′ x − ωt). Find the relation between k′ and k and then use conservation of energy to find the amplitude A′ on the far right. You may find it helpful to use the result of Problem 4.4 (S(x, t) = −τẏy′).