Question

Obtain an expression for practical determination of end correction for a pipe open at both ends.

Answer 1

In a pipe that is open at both ends, the fundamental frequency corresponds to the formation of an antinode at both ends and a node at the center.

Resonant Length Condition:

For the fundamental mode, the wavelength is:

`L+2e = λ/2`

Since v = fλ, we get:

λ = `(2(L+2e))/1`

`f = v/(2(L+2e))`

where:

• L = length of the pipe
• e = end correction at each open end
• v = velocity of sound
• f = fundamental frequency

Thus, the total end correction for a pipe open at both ends is 2e.

From experimental measurements, e ≈ 0.6R (where R is the radius of the pipe).