What do you mean by Open Organ Pipes ? Discuss theformation-of standing waves in open organ-pipe,

Explanation

An open organ pipe is a cylindrical tube which is open at both ends.
Formation of standing waves in open organ pipe

Consider an open organ pipe PQ in which incident wave travels from P to Q. The equation of incident wave is:
`y_(1) = A sinn (2pi)/(lambda vt-x)`..(i)
and equation of reflected wave travelling from Q to P is
`y_(2) = A sin (2pi)/lambda (vt+x)`........(ii)
The phase change of reflected wave is zero in case of open organ pipe, so equation of stationary wave formed is
`y =y_(1) + y_(2)`.........(iii)
Using equation (i) and (ii) in equation (iii) we have
`y=2[sin (2pi)/lambda(vt-x)] + sin (2pi)/lambda [vt +x]`....... (iv)
Using trigonometric identity
`sin C + sin D = 2sin ((C+D)/2) cos (C-D)/2` in equation (iv), we have
`y=2A sinn((2pivt)/lambda) cos ((2pi)/lambdax) [therefore cos -(theta) = cos theta]`
So, `y=A. sin((2pivt)/lambda)`. Here, A. = Amplitude of stationary wave formed `=2A cos((2pi)/lambda x)`
Therefore equation of stationary wave in open organ pipe is `y= A. sin((2pivt)/lambda)`