Standing wave pattern on a string is described by the equation below, where x and y are in meters and t is in seconds: y(x,t) = 0.051 (sin 9nx) (cos 56t). Use nonnegative values for x. (Use x ≥ 0.)
(a) Where is the node with the smallest value of x?
(b) Where is the node with the second smallest value of x?
(c) Where is the node with the third smallest value of x?
(d) What is the period of the oscillatory motion of any (nonnode) point?
Consider the two traveling waves that interfere to produce this wave:
(e) What is the speed of these traveling waves? (in m/s)
(f) What is the amplitude of these traveling waves?
Consider the times t ≥ 0 when all points on the string have zero transverse velocity:
(g) For t = 0, what is the first time that all points on the string have zero transverse velocity?
(h) What is the second time that this occurs?
(i) What is the third time that this occurs?