One dimensional wave equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{\partial^2 u}{\partial t^2} = c^2\frac{\partial^2 u}{\partial x^2}[/tex]

Where c is the vertical velocity of the vibrating string.

This will give D'Alembert solution of [tex]u(x,t) = \frac{1}{2}[f(x+ct) + G(x+ct)] + \frac{1}{2}[f(x+ct) + G(x+ct)][/tex]

Where [tex]u(x,t) = \frac{1}{2}[f(x+ct) + G(x+ct)][/tex] is the wave moving left with velocity c and [tex]\frac{1}{2}[f(x+ct) + G(x+ct)][/tex] is wave moving right with velocity c.

From the above, this mean the vertical velocity ( lets call u(x,t) axis ) of the vibrating string is the same as the propagating ( along x axis ) velocity of the wave.

Question:

1) If the string is vibrating in the fundamental frequency ( single freq.). The velocity at different point is different because every point is vibrating at the same frequency and the point in the middle travel a farther distance than the points close to the end.

2) Is it really true the propagation velocity same as the vibrating velocity?

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# Velocity in D'Alembert solution is the same as virtical velocity?

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