The pattern of standing waves formed on a stretched strinig at two instants of time are shown in figure. The velocity of two waves superimposing to form stationary wave is `360ms^(-1)` and their frequencies are 256 Hz.
(a) Calculate the time at which the second curve is plotted. ltbr. (b) Mark nodes and antinodes on the curve.
(c) Calculate the distance between `A^(')` and `C^(')`.

Explanation

Given, v = 256 Hz
`therefore` Time period, `T = (1)/(v) = (1)/(256) s = 3.9 xx 10^(-3)`s
(a) Time to pass through mean position is
`t = (T)/(4) = (3.9 xx 10^(-3))/(4)`
`= 9.8 xx 10^(-4)`s
(b) Nodes are at A, B, C, D and E, where displacement is zero. Antinodes are at A', C' where displacement is maximum.
(c) From the graph, we find that the distance between A' and C' is equal to `2 (lambda)/(2) = lambda`
`therefore" "lambda = (upsilon)/(v) = (360)/(256) = 1.41` m