Wave equation in classical mechanics

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In summary, the wave equation is a fundamental equation in classical mechanics that describes the behavior of waves. It is a second-order partial differential equation that relates the second derivative of a wave's position to its acceleration and the wave's propagation speed. It is used to model a wide range of physical phenomena, including sound waves, electromagnetic waves, and quantum particles. The wave equation has been extensively studied and has played a crucial role in advancing our understanding of the physical world.
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DeNiSkA
My question is about equation of a wave which travels on a string.
I have seen that we write wave function as y=f(x-vt) , but why did we select this function, why not any other like y=f(5x-9vt) .
I also have a question why is there a negative sign why not positive sign, (for me positive one makes sense)

Thank you for helping :)
 
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