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Tane Waves A plane wave is described mathematically by D(x, t) = A sin (kz - wt + 8), (1) where A is the amplitude of the wave, k is the wavenumber which is the number of complete waves per unit distance, w is the angular frequency, which is the number of radians per unit time, and 8 is a phase angle, which becomes important when we add more than one plane wave. Two waves are said to be in-phase if they have the same value of 6. Other quantities of interest are (frequency in hertz or cycles per second) (2) 2T A = (wavelength in meters = distance between two peaks) (3) 1 2T T = == (period in seconds = duration between two peaks) (4) W v=xf = 7 (wave speed). (5) Answer the following questions. (a) For the wave shown in Figure 1, approximate w, f, T, and 6, and explain your results. D(x = 0,1) 10 0 И t(s) 2s 4 s -10 FIG. 1. Displacement versus time at z = 0 for a wave on a string. (b) If the wave in Figure 1 is moving to the right with a speed of 2.0 m/s make a plot of the displacement D versus position z at t=0 which includes two peaks. What is the wavelength A and wavenumber k? Explain your reasoning and label your axes.