A transverse wave on a stretched string is mathematically represented by
y(x,t)=0.05cos(2πx+100πt)
where x is in metres and t in seconds.
(i) State the general criterion that allows you to identify the direction of propagation of a sinusoidal wave written in the form y(x,t)=Asin(kx±ωt+ϕ).
(ii) Using the criterion stated in part (i), determine whether the given wave travels towards the +x–direction or the −x–direction.
(iii) Write an explicit equation for a wave having the same amplitude, angular frequency and initial phase as the above wave but propagating in the opposite direction along the string.