In an organ pipe (may be closed or open ) of `99 cm` length standing wave is set up , whose equation is given by longitudinal displacement.

`xi = (0.1 mm) cos ( 2pi)/(0.8) (y + 1 cm) cos (400) t`where `y` is measured from the top of the tube in `metres` and `t "in" seconds` . Here `1 cm` is the end correction.
The upper end and the lower end of the tube are respectively .

Options

A. open - closed
B. closed - open
C. open - open
D. closed - closed

Answer

A

Explanation

`xi = (0.1 mm) cos ( 2pi)/( 0.8) ( y + 1 cm) cos (400 t)`
End correction is `1 cm` , so at `y = - 1 cm`
`xi = (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`
`xi = (0.1 mm) cos ( 2pi)/( 0.8) (0.99 + 0.01)`
`= 0.01 cos ( 5 pi)/(2) = 0` `rArr` Node
So tube is open closed.