*Separation of variables boundary condition. Consider sound waves in an open pipe of length L. Call the longitudinal displacement of the air ). An explosive device launches the sound waves at = 0, so the initial displacement is zero but the initial velocity is a non-zero function f(z, = 0). Follow steps 6-8 of the \"separation of variables procedure\" to write a solution for )(z, t) as a sum of normal modes. . Use BCs to eliminate constants. . Write simplified solution as product of nonzero functions. . Use remaining BCs to find acceptable _ values of the separation constant