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Find the End Correction for the Pipe Open at Both the Ends In Fundamental Mode. - Physics

Find the end correction for the pipe open at both the ends in fundamental mode.

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Solution

End correction in open pipe:

i.  Let,
l1 and l2 = Vibrating lengths of pipe
n1 and n2 = Resonating frequency
v = Velocity of sound
e = End correction

ii.  For the first resonance,

`n_1=v/(2(l_1+2e))`

`v=2n_1(l_1+2e)` ...............(1)

 iii.  For the second resonance,

`n_2=v/(2(l_2+2e))`

`v=2n_2(l_2+2e)` ...............(1)

iv.  From (1) and (2),

`n_1(l_1+2e)=n_2(l_2+2e)`

`n_1l_1+2en_1=n_2l_2+2en_2`

`2en_1-2en_2=n_2l_2-n_1l_1`

`2e(n_1-n_2)=n_2l_2-n_1l_1`

`e=(n_2l_2-n_1l_1)/(2(n_1-n_2))=(n_1l_1-n_2l_2)/(2(n_2-n_1))`

Concept: Study of Vibrations of Air Columns
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