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.
Equation of the standing wave in terms of excess pressure is ( take bulk modulus ` = 5 xx 10^(5) N//m^(2)`))

Options

A. `P _(ex) = (125 pi N//m^(2)) sin ( 2pi)/(0.8) ( y + 1 cm) cos (400 t)`
B. `P _(ex) = (125 pi N//m^(2)) cos ( 2pi)/(0.8) ( y + 1 cm) sin (400 t)`
C. `P _(ex) = (225 pi N//m^(2)) sin ( 2pi)/(0.8) ( y + 1 cm) cos (200 t)`
D. `P _(ex) = (225 pi N//m^(2)) cos ( 2pi)/(0.8) ( y + 1 cm) sin (200 t)`

Answer

A

Explanation

`P_(ex) = - B( d xi)/(d x)`
`= ( 5 xx 10^(5)) xx (0.1 xx 10^(-3)) ( 2pi)/(0.8) sin ( 2pi)/(0.8) ( y + 1 cm) cos (400) t`
` = (125 pi N//m^(2)) sin ( 2 pi)/(0.8) ( y + 1 cm) cos (400 t)`