- #1
jk22
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The solution for the wave equation with initial conditions $$u(x,0)=f(x)$$ and $$u_t(x,0)=g(x)$$
Is given for example on wikipedia : $$u(x,t)=(f(x+ct)+f(x-ct)+1/c*\int_{x-ct}^{x+ct}g(s)ds)/2$$
So a vibrating string, since there is no conditions on ##g## (like ##\sqrt{1-g(x)^2/c^2}##), could move transversally at speed bigger than c, while the movement along the rope is at speed c ?
<mentor fix latex>
Is given for example on wikipedia : $$u(x,t)=(f(x+ct)+f(x-ct)+1/c*\int_{x-ct}^{x+ct}g(s)ds)/2$$
So a vibrating string, since there is no conditions on ##g## (like ##\sqrt{1-g(x)^2/c^2}##), could move transversally at speed bigger than c, while the movement along the rope is at speed c ?
<mentor fix latex>
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