1.

In an organ pipe ( may be closed or open of `99 cm` length standing wave is setup , whose equation is given by longitudinal displacement `xi = (0.1 mm) cos ( 2pi)/( 0.8) ( y + 1 cm) cos 2 pi (400) t` where `y` is measured from the top of the tube in `metres and t "in second"`. Here `1 cm` is th end correction. The upper end and the lower end of the tube are respectively :A. open - closedB. closed - openC. open - openD. closed - closed

Answer» Correct Answer - A
`(0.1 mm) cos ( 2pi)/(0.8) ( y + 1 cm ) cos 2 pi 7 (400) t`
end correction is `1 cm`. So at `y = - 1 cm`.
`(0.1 mm) cos ( 2 pi)/(0.8) ( - 1 cm + 1 cm) = ( 0.1 mm) cos (0) =` Antinode
So upper end is open.
At lower end `y = 99 cm = 0.99 m`
`= (0.1 mm) cos ( 2 pi)/( 0.8) (0.99 + 0.01)`
` = 0.01 cos ( 5 pi)/(2) = 0 rArr` Node
So tube is open closed.


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