Equation (15.7) for a sinusoidal wave can be made more general by including a phase angle Ф, where 0≤Ф≤2 π (in radians). Then the wave function y(x, t) becomes y(x, t) = Acos (kx - wt +Ф)
(a) Sketch the wave as a function of x at t = 0 for Ф = 0, Ф = π /4, Ф = π /2, Ф = 3'π/4, and Ф = 3 π /2.
(b) Calculate the transverse velocity uy= ay/at.
(c) At t = 0, a particle on the string at x = 0 has displacement y = A√/Y2. Is this enough information to determine the value of Ф? In addition, if you are told that a particle at x = 0 is moving toward y = 0 at t = 0, what is the value of Ф?
(d) Explain in general what you must know about the wave's behavior at a given instant to determine the value of Ф