# 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.

#### 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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