1. Consider transverse standing waves on a stretched string of length / that is attached to fixed supports at both ends. Let v be the phase velocity of the waves. (a) What is the wavelength and frequency (in Hertz) of the standing wave with the longest wavelength? What is the wavelength and frequency (in Hertz) of the standing wave with the next longest wavelength? (b) Suppose that the string extends from x = 0 to x = 1. Let y(x, t) be the transverse displacement. What is the most general expression for y(x, t)? (c) Suppose that y(x, 0) = a sin in (7 717) + (77) +b sin sin (27 ½), ay(x, 0) = 0. at Here, a and b are constants. Determine y(x, t) for all > 0.