1-D wave resonance in the case of an Open-Ended String

[Another]

Homework Statement

I want to know the conditions in the case of Open-End.

Relevant Equations

$\frac{1}{v^2} \frac{∂^2y}{{∂t}^2} = \frac{∂^2y}{{∂x}^2}$ and general solution $y = A sin(kx+ωt)+ B cos(kx+ωt)$

$\frac{1}{v^2} \frac{∂^2y}{{∂t}^2} = \frac{∂^2y}{{∂x}^2}$ and general solution $y = A sin(kx+ωt)+ B cos(kx+ωt)$

http://blogs.bu.edu/ggarber/archive/bua-py-25/waves-and-sound/standing-waves-in-strings-and-pipes/
In case fixed at both ends The condition is $y(0,t) = 0$ and $y(L,t) = 0$

But i don't know The condition in a case Open-End of string. So I can't solve the problem.

 

[kuruman]

Try $$\left. \frac{\partial y}{\partial x} \right|_{x=L} =0.$$

 

[Another]

Try $$\left. \frac{\partial y}{\partial x} \right|_{x=L} =0.$$

if free string both ends. The condition is $\left. \frac{\partial y}{\partial x} \right|_{x=L} =0.$ and $\left. \frac{\partial y}{\partial x} \right|_{x=0} =0.$ ?

 

[kuruman]

View attachment 242686

if free string both ends. The condition is $\left. \frac{\partial y}{\partial x} \right|_{x=L} =0.$ and $\left. \frac{\partial y}{\partial x} \right|_{x=0} =0.$ ?

Yes.