A progressive wave travelling along a string has maximum amplitude A = 0.0821 m, angular frequency w = 100 rad/s and wave number k = 22.0 rad/m. If the wave has zero amplitude at t = 0 and x = 0 for its starting conditions (i) State the wave function that represents the progressive wave motion for this wave travelling in the negative x-direction. (ii) State the wave function for this wave travelling in the positive x-direction. (iii) Find the wavelength (L), period (T ) and the speed (v) of this wave. (iv) Find its amplitude at a time t = 2.5 s at a distance x = 3.2 m from its origin, for this wave travelling in the negative x-direction.