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In an organ pipe ( may be closed or open...

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

A

`P_(ex)=(125 piN//m^2)sin (2pi)/0.8 (y+1cm) cos 2pi (400t)`

B

`P_(ex)=(125 piN//m^2)cos (2pi)/0.8 (y+1cm) sin 2pi (400t)`

C

`P_(ex)=(225 piN//m^2)sin (2pi)/0.8 (y+1cm) cos 2pi (200t)`

D

`P_(ex)=(225 piN//m^2)cos (2pi)/0.8 (y+1cm) sin 2pi (200t)`

Text Solution

Verified by Experts

`P_(ex)=-B(dphi)/(dx)`
`=(5xx10^5) xx (0.1xx10^(-3))(2pi)/0.8 sin (2pi)/0.8 (y+1cm)cos 2pi (400)t`
`=(125 pi N//m^2) sin (2pi)/0.8 (y+1cm)cos 2pi(400t)`
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