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    A stretched string occupies the semi-infinite interval -infinity<x<=0.
    y(x,t) := f(x-ct) + f(-x-ct) is a solution of the wave equation.

    What boundary condition does y satisfy at x=0? Is this just y(0,t) = 2f(-ct)?

    Describe what is going on in terms of incident and reflected waves. At x=0, the displacement varies as a function of time so the end is not fixed. However, I'm unsure about how this relates to incident and reflected waves.

    (I worked out that if y(x,t) = f(x-ct) - f(-x-ct) then f(x-ct) represented the incident wave and -f(-x-ct) represented the reflected wave.)
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    i think it might clear things up if you consider a tethered string with boundary condition y=0 (y being the vertical displacement).

    you are still correct about the different parts representing incident and reflected waves though.
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    If y = 0 then do we not have the equation y(x,t) = f(x-ct) - f(-x-ct)? I'm sorry I don't really know what you mean.
 
 
 
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