1. The problem statement, all variables and given/known data Show that the solution of the form ρ1 = ρ1(x±a0t) satisfy the equation: ∂2ρ1/∂t2 - a02∂2ρ1/∂x2 = 0 and that they correspond to waves propagating in the directions x increasing or decreasing. 2. Relevant equations P = P0 + P1 ρ = ρ0 + ρ1 u = u1 3. The attempt at a solution P1 = nKρ0n-1ρ1 ≡ nP0/ρ0 * ρ1 We shall define a quantity a02 = n * P0/ρ0. a0 has dimensions of velocity and is a constant. The linearized form of the continuity equation is: 1/ρ0 * ∂ρ1/∂t + ∂u1/∂x = 0 The linearized form of the momentum equation is: ∂u1/∂t = -1/ρ0 * ∂P1/∂x This is as far as I have gotten with the problem. This problem can be found in the book of the physics of the interstellar medium by Dyson and Williams. Any help and I would be grateful!