The string fixed at both ends has a length L = 1.2 m, diameter d = 0.5 mm, and density p = 7800 kg/m; see Fig below. Let the vibration of the string in the y direction be denoted as W(x,t). Answer the following questions. (A) [6/30] Explain why the natural frequency, @, n = 1, 2, ..., for a string fixed at both ends must satisfy_sin(@L/c) = 0 where c = t/pa and a is the cross-sectional area of the string. (B) [4/10] Find the string tension so that the third natural frequency is 6 Hz. (C) [10/30] Assume the string is released from rest and from the configuration W(x,0) = 0.2x for x 0.6 and 0.24 -0.2x for 0.6 < x 1.2. Find the free vibration W(x,t).