#### Question

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))`

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Solution for question: Find the End Correction for the Pipe Open at Both the Ends In Fundamental Mode. concept: null - Study of Vibrations of Air Columns. For the courses HSC Science (Electronics), HSC Science (General) , HSC Science (Computer Science)