Question: At time t, the displacement of a point on a vibrating guitar string stretched between x = 0 and x = π is given by
f(x,t) = cos t sin x, 0 ≤ x ≤ Π, 0 ≤ t ≤ 2Π
(a) Sketch the cross-sections of this function with t fixed at t = 0, π/4 and the cross-sections with x fixed at x = π/4, π/2.
(b) What is the value of f if x = 0 or x = π? Explain why this is to be expected.
(c) Explain the relation of the cross-sections to the surface representing f.