The nodes of a standing wave are points at which the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example, that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move). Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(z, t) = Asin(kz) sin(wt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wave number, w is the angular frequency of the wave, and is time. Part A Which one of the following statements about such a wave as described in the problem introduction is correct? O This wave is traveling in the +z direction. O This wave is traveling in the z direction. O This wave is oscillating but not traveling. O This wave is traveling but not oscillating. Request Answer Part B Attime = 0, what is the displacement of the string y (z, 0)? Express your answer in terms of A, k, and other previously introduced quantities. r*C)? y(z,0) = Request Answer v Part C What is the displacement of the string as a function of x at time T/4, where T is the period of oscillation of the string? Express the displacement in terms of A, x, k, and other constants; that is, evaluate w% and substitute it in the expression for y (z, t). P View Available Hint(s) gy 6 2 O = ? y(z, %) =14 cos (kx) Previous Answers X Incorrect; Try Again; 5 attempts remaining PartD At which three points 1, 2, and 3 closest to 2 = 0 but with > 0 will the displacement of the string y (z, t) be zero for all times? These are the first three nodal points. Express the first three nonzero nodal points in terms of the wavelength . List them in increasing order, separated by commas. You should enter only the factors that multiply A. Do not enter \\ for each one. P View Available Hint(s) 600 T1, T2, T3 = A