1. The problem statement, all variables and given/known data "Solve the wave equation with the following initial conditions and boundary conditions." ∂2Y/∂x2 = 1/v2 * ∂2Y/∂t2 Boundary conditions: ∂Y/∂x(x=0, t)=0 and Y(x=L,t)=0 Initial Conditions: ∂Y/∂t(x, t=0) = 0 Y(x,t=0) = δ(x-L/2) 2. Relevant equations Using separation of variables: Y(x,t) = X(x)*T(t) X(x) = C*cos(kx/L) + D*sin(kx/L) T(t) = E*cos(wt) + F*sin(wt) 3. The attempt at a solution So, I'm relatively familiar with this process but I have a couple of hangups relating to these specific initial conditions. First, the requirement that the partial of y with respect to x=0 at all times t (first boundary condition) seems, to me, to make a wave impossible. It gives D=0 AND C=0 OR k=0, but of course all of these are unsatisfactory solutions. More analytically, it seems that requiring the slope to always be 0 at x=0 is really restricting that piece of the wave from moving. I'm just not sure how to handle it. Moving past that though (I assumed y(x=0,t)=0 as my first boundary condition giving C=0), I'm also not sure how to handle the initial condition. The initial condition equation, x-L/2, has an integral of 0 when integrated from 0 to L. This makes sense since the expression has equal area above and below y=0, but I still don't know how to handle it in terms of getting an actual solution. Just thinking out loud as I type this, does the delta in the expression indicate that I should be treating it as an absolute value equation so that all of it is forced to be above y=0?