Two waves travelling in opposite directions produce a standing wave. The individual wave functions are given by y₁ = 4sin (3x - 2t) cm and y₂= 4sin (3x + 2t) cm, where x and y are in cm and t in s (sin 6.9 = 0.578)

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The maximum displacement of the x = 2.3 cm is 4.63 cm

The maximum displacement of the motion at x = 2.3 cm is 5.32 cm

odes are formed at x value given by 0, $\frac{π}{3}, \frac{π 2}{3}, π, \frac{7 π}{3}, \dots \dots$

Antinodes are formed at x values given by $\frac{π}{6}, \frac{π}{2}, \frac{5 π}{6}, \frac{7 π}{6}, \dots \dots$

answer is A, C, D.

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Detailed Solution

Resulting wave equation will be y = 8sin3x cos2t = Rcos2t
R = 8sin3x
At x = 2.3 we use R = 8sin(6.9) = 8 x 0.578 = 4.63
Nodes (R = 0) are obtained where sin 3x = 0
$\Rightarrow x = 0, \frac{π}{3}, \frac{2 π}{3}, \dots \dots \dots$
Antinodes (R = 8cm) are obtained where sin (3x) = $\pm$ 1
$\Rightarrow x = 0, \frac{π}{6}, \frac{π}{2}, \frac{5 π}{6}, \dots \dots \dots$