The displacement of a wave travelling along a rope is given by
y=0.02cos(0.50x+120t)
where y and x are measured in metres and t in seconds.
(i) State whether the wave propagates in the positive or the negative x–direction. Give a reason based solely on the given equation.
(ii) Derive an expression for the speed of this wave in symbolic form using the parameters that appear in the equation.
(iii) Calculate the numerical value of the speed of the wave.
(iv) Determine the wavelength of the wave and verify that the numerical values obtained in parts (iii) and (iv) satisfy the relation v=λf. (Take 2π≈6.28.)