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 air column is vibrating in

Options

A. first overtone
B. second overtone
C. third overtone
D. fundamental mode

Answer

B

Explanation

`( 2pi)/(0.8) = ( 2 pi)/(lambda)` so `lambda = 0.8`
And effective length of air column ` = 0.99 + 0.01 = 1 m`
So `(l)/(lambda) = (5)/(4)`
` l = 5(lambda)/(4)`
so five loops will be formed
` l = 5(lambda)/(4)`
so second overtone.