(a) Sketch the first and second harmonic standing waves on a stretched string of length L . Deduce an expression for the frequencies of the family of standing waves that can be excited on the string. (b) The wave function of a standing wave on a string that is fixed at both ends is given in SI units by y(x,t) = (0.024) sin(62.8x) cos(471t). Find the speed of the waves on the string, and the distance between nodes for the standing wave. [hint: You may need to use sin T1 + sin T2 = 2 cos 1/2 (T2-T1 ) sin 1/2 (T1 + T2)].