Question

The equation of a transverse wave traveling along a string is y = 0.419 sin(0.265x - 18.90), in which x and y are in meters and t is in seconds. (a) What is the displacement y at x = 6.36 m, t = 0.582 s? (Hint: Displacement is a vector quantity. Pay attention to the sign.) -.0442 m(b) Choose an equation of a wave that, when added to the given one, would produce standing waves on the string. O V'(x,t) = (0.419) sin(0.265x + 18.9t) O y'(x,t) = (0.210)sin(0.13x + 18.9t) O y'(x,t) = (0.419)sin(0.265x - 6.36) O y(x,t) = (0.419)sin(0.265x + 6.3t) O none of these O ''(x,t) = (-0.419) sin(0.265x - 18.9t) (c) What is the displacement of the resultant standing wave at x = 6.36 m, t = 0.582 s? .031 Xm

Answer 1

a)
b)

c) Displacement of the resultant standing wave,

y_net = y(x,t) + y'(x,t)

= 0.419*sin(0.265*x - 18.9*t) + 0.419*sin(0.265*x + 18.9*t)

at x = 6.36 m, t = 0.582 s

y_net = 0.419*sin(0.265*6.36 - 18.9*0.582) + 0.419*sin(0.265*6.36 + 18.9*0.582)

= 0.00352 m <<<<<<------------Answer

Note : use calculator in radian mode.