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

Two waves travelling in opposite directions produce a standing wave .

1.	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
Answer» (a) When the two waves are summed. The result is a standing wave whose mathematical representation is given by Equation, with `A = 4.0 cm` and `k = 3.0 rad//cm,` `y = (2A sin kx)cos omegat = [(8.0 cm) sin 3.0 X] cos 2.0 t` Thus, the maximum displacement of a particel at the position `x = 2.3 cm` is `y_(max) = [(8.0 cm) sin 3.0x]_(x = 2.3 cm)` `= (8.0 m) sin (6.9 rad) = 4.6 cm` (b) Because `k = 2pi//lambda = 3.0 rad//cm`, we see that `lambda = 2pi//3cm`. Therefore, the antinodes are located at `x = n((pi)/(6.0)) cm (n = 1, 3, 5, ........)` and the nodes are located at `x = n(lambda)/(2-)((pi)/(3.0)) cm (n = 1, 2, 3, .........)`

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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

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