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**1. The problem statement, all variables and given/known data**

Solve the initial boundary value problem

[tex]u_{tt}=c^2u_{xx}[/tex]

[tex]u(-a,t)=0,\quad u(a,t)=0,\quad u(x,0)=\sin(\omega_1 x)-b\sin(\omega_2x) [/tex]

where [itex]a, b, \omega_1, \omega_2[/itex] are positive constants.

**2. Relevant equations**

d'Alembert's solution

**3. The attempt at a solution**

Are these initial/boundary conditions enough to fully solve the problem? All of the text books I have seen address only the case where [itex]u(x,0)[/itex] and [itex]u_t(x,0)[/itex] is also given. Or possibly d'Alembert's general solution is not good to use here? Thanks all!