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The expression for a standing wave is y...

The expression for a standing wave is ` y(x, t) = 2 sin ( 0 . 1 pi x) cos 100 pi t ` , where x, y are in cm and t is in second. Find the distance between a node and the next antinode of the wave .

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` y (x, y) = 2 sin ( 0 . 1 pi x) cos 100 pi t = a sin kx cot omega t `
Here, ` k = 0 . 1 pi, omega = 100 pi `
So, ` lambda = (2pi)/(k) = (2pi)/(0 . 1 pi) = 20 cm `
So, separation between a node and the next antinode
` = (lambda)/(4) = 5` cm
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