Boundary conditions for wave fixed at one end

[mrausum]

For a string fixed at x=0 and free at x=l I know $$\frac{dy}{dx}(l,t)=0$$ (d's are meant to be partials) but what is the other boundary associated with the end of the string? Is the second derivative also equal to 0?

 

[djeitnstine]

$$\frac{\partial y(0,t)}{\partial x}=0$$ must also be true since it is fixed. Also $$\frac{\partial^2 y(0,t)}{\partial x^2}=0$$