You and your friend create a travelling wave on a string and decide to study its properties in two ways. Your friend watches the particle at x = 1 m and records its displacement as a function of time. You snap a photo of the wave at t = 1 s. The resulting graphs are shown below. x=1m A 2 t=1s 1 (s) 1.5 x (m) (a) Is this wave travelling to the right or left? Explain how you know in words. (b) Write down the full equation for this wave in the form D (x, t) = A sin (kxwt + 0). (c) What is the wave speed of this wave? Suppose you want to create a travelling wave with double the wave speed of this wave but the same frequency - what would its wave equation be? Explain your answer. m/s (d) What is the transverse velocity (particle speed) of the black dot at t = 1 s? Suppose you wanted to create a travelling wave with double the particle speed for the black dot at t = 1 s, but without changing the amplitude - what would its wave equation be? Explain your answer.