A sinusoidal wave travels along a stretched string. A photograph of the string at a certain instant shows that the distance between successive crests is 32cm. At a fixed point P on the string the displacement–time record indicates that 20 complete oscillations are completed in 4.0s. The maximum displacement of any point of the string from equilibrium is 2.0cm.
(i) Calculate the wavelength of the wave.
(ii) Determine the period and the frequency of oscillation at point P.
(iii) Find the speed with which the wave propagates along the string.
(iv) Obtain the ratio of the maximum speed of a particle of the string to the speed of the wave itself, and comment on whether this ratio depends on the amplitude.