Hi there. I was trying to understand this deduction of the one dimensional wave equation developed at the beggining of the book A first course in partial differential equations of H.F. Weinberger.(adsbygoogle = window.adsbygoogle || []).push({});

You can see it right here: http://books.google.com.ar/books?hl...2eHPnArCVnLC7Q0FtHljNwcV7g#v=onepage&q&f=fals

I'm having a problem with the part where he consideres the tension over the string. I don't know how this expression is deduced. The book says: We now consider an arbitrary portion [tex]s_1\leq s\leq s_2[/tex] of the string. Taking the components of the tensile force in the x-direction, we find that the total force in the x-direction acting on this portion is:

[tex]\frac{ T(s_2,t)\frac{\partial x}{\partial s}(s_2,t) }{ \sqrt { \left ( \frac{\partial x}{\partial s}\right )^2+\left( \frac{\partial y}{\partial s}\right )^2}}-\frac{ T(s_1,t)\frac{\partial x}{\partial s}(s_1,t) }{ \sqrt { \left ( \frac{\partial x}{\partial s}\right )^2+\left( \frac{\partial y}{\partial s}\right )^2}}[/tex]

The whole problem for me now is just this thing. I think I understand a bit what this equation says, but perhaps some one could help me to figure this out more clearly. At first, T is some function, lets say a function force that depends on the material, and as we stretch it or compress, as a spring, it produces a reaction. Ok. Then the denominator is the arc lenght formula, so its saying how much we stretched or compressed the string. And the other thing is the derivative of the curve, and I think its there because the force goes tangential to the string. Is this lecture right?

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# Homework Help: One dimensional wave equation

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