Past exam of the mathematical methods II course of the University of Oxford / 2019 resit / 1 / Solution

Convert the fixed position to $x=0.20\mathrm{m}$. The element's displacement is then $y(t)=0.27\sin (2.4-500t)\mathrm{mm}$. Taking time derivatives at fixed position gives its transverse velocity and acceleration:Equivalently the prefactors in SI units are $-0.135\mathrm{m}{\mathrm{s}}^{-1}$ and $-67.5\mathrm{m}{\mathrm{s}}^{-2}$. The phase is measured in radians. At $t=4\mathrm{s}$,These are the transverse motions of the material element, not the propagation speed of the wave along the string.