Two waves travelling in opposite directions produce a standing wave . The individual wave functions are given by `y_(1) = 4 sin ( 3x - 2 t)` and `y_(2) = 4 sin ( 3x + 2 t) cm` , where `x` and `y` are in cm

Options

A. The maximum displacement of the motion at x = 2.3 cm is 4.63 cm
B. The maximum displacement of the motion at x = 2.3 cm is 5.32 cm
C. Nodes are formed at x values given by `0,(pi)/(3), (2pi)/(3), pi, (4pi)/(3)`
D. Antinodes are formed at x values given by `(pi)/(6), (pi)/(2), (5pi)/(6),(7pi)/(6)`

Answer

A, C, D

Explanation

Resulting wave equation will be `y = 8sin 3x cos 2t = R cos 2t`
x = 2.3 we use R = sin (6.9) = 6.63 cm
Nodes (R = 0) are obtained where sin(3x) = 0
`x = 0, (pi)/(3), (2pi)/(3)`
Antinodes (R = 8 cm) are obtained where sin(3x) = pm 1
`x = (pi)/(6), (pi)/(2), (5pi)/(6)`...