A stretched rope carries a progressive sinusoidal wave. The displacement–position graphs are observed at two instants.
• At t=0, two successive crests are located at x=0.15m and x=0.55m.
• At t=5.0ms, the same two crests are found at x=0.05m and x=0.45m.
Assume all displacements are transverse and that the amplitude of the wave is 2.0cm.
(i) Calculate the wavelength of the wave.
(ii) Determine the speed and the direction in which the wave is propagating.
(iii) Using your results from parts (i) and (ii), find the frequency of the wave.
(iv) Taking the phase to be zero at x=0 when t=0, write the simplest mathematical expression for the displacement y(x,t) of the wave.