Two waves traveling in opposite directions along a string fixed at both ends create a standing wave described by y(x, t) = 0.01 sin(36x)cos(1090t). The string has a linear mass density of 0.01 kg/m, and the tension in the string is supplied by a mass hanging from one end. If the string vibrates in its third harmonic, calculate the following.
a) the length of the string
b) the velocity of the waves
c) the mass of the hanging mass