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The resultant displacement due to superp...

The resultant displacement due to superposition of two identical progressive waves is
` y = 5 cos ( 0 . 2 pi x) sin (64 pi t )` , where x , y are in cm and t is in sec . Find the equations of the two superposing waves .

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Resultant displacement due to superposition of two identical progressive waves ,
` :. Y = 5 cos ( 0 . 2 pi x) sin (64 pi t )`
`= (5)/(2) xx 2 cos ( 0 . 2 pi x) sin (64 pi t) `
` = (5)/(2) [ sin (64 pi t + 0 . 2 pi x) + sin (64 pi t - 0 . 2 pi x)] `
So, expression of those progressive waves are as follows,
` y_(1) = 2 . 5 sin (64 pi t + 0 . 2 pi x) `
and ` y_(2) = 2 . 5 sin (64 pi t - 0 . 2 pi x) `
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