A transverse wave on a stretched string is described by
y(x,t)=0.05sin(0.402πx−50πt)m
where x is in metres and t in seconds.
(i) Calculate the instantaneous displacement of the particle at x=0.10m and t=0.015s.
(ii) Determine the instantaneous velocity of this particle at the same instant.
(iii) Find the instantaneous acceleration of the particle at the same instant.
(iv) Compare the magnitude of the particle’s instantaneous velocity with the speed of the wave and state which is greater at that instant.