I am a high school student and recently heard of S. R. so I am excited to know what are its effect on sine wave in a string. Is there any change in wavelength, frequency , interference pattern etc.
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$\begingroup$ If you mean an everyday object like a violin string, the effects are negligible. $\endgroup$– G. SmithCommented Apr 7, 2021 at 3:01
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$\begingroup$ Imagining a special string in which wave move at speed comparable to light. $\endgroup$– Rajshekhar SinghCommented Apr 7, 2021 at 3:42
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I am also interested and now studying SR and GR. From my viewpoint, in the ideal case(ignore the effect of gravity), the vibration equation of a string is $$\begin{equation} \begin{array}{ll} \frac{\partial^{2} u}{\partial t^{2}}-a^{2} \frac{\partial^{2} u}{\partial x^{2}}=0, & -\infty<x<\infty, t>0\\ \left.u(x, t)\right|_{t=0}=\phi(x), & -\infty<x<\infty \\ \left.\frac{\partial u}{\partial t}\right|_{t=0}=\psi(x), & -\infty<x<\infty \end{array} \end{equation}$$ notice that in equation there is $a^2$, where $a$ is the speed of wave, which implies that the information of a certain point in a string can not reach arbitrary point with infinite speed,to be specific,one can get the solution of $$\begin{equation} u(x, t) =\frac{1}{2}[\phi(x-a t)+\phi(x+a t)]+\frac{1}{2 a} \int_{x-a t}^{x+a t} \psi(\xi) \mathrm{d} \xi . \end{equation}$$
$\phi(x)$is the initial excited wave at t=0. the solution shows that vibration at x=x0 at t=0, then it will only effect the region:$[x-at,x+at]$ symmetrically. if you restric that the speed within the speed of light, then it obeys the SR.
