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Wave equation: intial conditions

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!
 
A second order partial differential equation requires four boundary conditions in order to be fully solved, so it might be the case that you are meant to assume that ut(x,0)=0. Is that all of the information the question gives you?
 

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