# What are relativistic effects on classical sine wave?

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.

• If you mean an everyday object like a violin string, the effects are negligible. Commented Apr 7, 2021 at 3:01
• Imagining a special string in which wave move at speed comparable to light. Commented Apr 7, 2021 at 3:42

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 $$$$\begin{array}{ll} \frac{\partial^{2} u}{\partial t^{2}}-a^{2} \frac{\partial^{2} u}{\partial x^{2}}=0, & -\infty0\\ \left.u(x, t)\right|_{t=0}=\phi(x), & -\infty notice that in equation there is $$a^2$$, where $$a$$ is the speed of wave, which implies that the information of a certain point in a string can not reach arbitrary point with infinite speed,to be specific,one can get the solution of $$$$u(x, t) =\frac{1}{2}[\phi(x-a t)+\phi(x+a t)]+\frac{1}{2 a} \int_{x-a t}^{x+a t} \psi(\xi) \mathrm{d} \xi .$$$$
$$\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.