A wave on a string is described by y(x, t) = A cos(kx – ?t). (a) Graph y, vy, and ay as functions of x for time t = 0. (b) Consider the following points on the string: (i) x = 0; (ii) x = ?/4k; (iii) x = ?/2k; (iv) x = 3?/4k; (v) x = ?/k; (vi) x = 5?/4k; (vii) x = 3?/2k; (viii) x = 7?/4k. For a particle at each of these points at t = 0, describe in words whether the particle is moving and in what direction, and whether the particle is speeding up, slowing down, or instantaneously not accelerating.

Solution 14E Step 1 of 9: The sign of v deyermines the direction of motion of a particle on the string . If v = 0 and a = / 0 the speed of the particle is increasing. y y If v y / 0 ,the speed of the particle speeds up If v and y have tye same sign and if v and a have dyfferent y speed of the particle slows down.