Problem 4. [A] At time t = 0, the position and transverse velocity of a string obeying the wave
equation are given by y(x) and v (x). Find an explicit expression for y(x,t) in terms of these
y
functions; this is called d’Alembert’s solution. (Hint: construct solutions with initial position y(x)
and zero initial velocity, and vice versa, and add them together. Your final answer should contain
an integral involving v .)
y