A sinusoidal transverse wave travels along a stretched string in the positive x-direction. The amplitude of vibration is 3.0 cm and the wavelength is 0.40 m. The speed of the wave along the string is 20 m s−1. At time t=0, the element of the string situated at the origin is passing through its mean position moving towards the positive y-direction.
(i) Calculate the wave number k and the angular frequency ω of the wave.
(ii) Using the data above, construct the equation y(x,t) that gives the transverse displacement y (in centimetres) as a function of position x (in metres) and time t (in seconds).
(iii) With the equation obtained in part (ii), determine the displacement of the element of the string located at x=0.15m at time t=0.010s."