open pipe
Summary
An open pipe is a tube open at both ends, so a standing sound wave has a displacement antinode at each end. Its resonant frequencies are fn = nv/2L for every integer n (all harmonics), unlike a pipe closed at one end, which gives only odd harmonics.
Detail
Meaning: An open pipe is open at both ends. A standing sound wave in it has a displacement antinode at each end, because air moves freely there. The fundamental therefore fits half a wavelength in the pipe (λ₁ = 2L), and every integer harmonic is allowed, both even and odd.
Equation: fn = nv/(2L), where fn is the frequency of the nth harmonic (Hz), n is a positive integer (unitless), v is the speed of sound in the air (m/s), and L is the pipe length (m).
On the MCAT: Passages use organ pipes, flutes, or a resonance tube and compare open with closed pipes. Expect to predict that a shorter pipe gives a higher frequency, that warmer air raises v and so raises f, and that a pipe of the same length closed at one end has a fundamental half as high (v/4L) with only odd harmonics. You may also count nodes: the nth harmonic of an open pipe has n displacement nodes.
Common confusion: Students treat the open end as a node. For displacement it is an antinode. For pressure it is the opposite: the pressure stays near atmospheric there, so it is a pressure node. Check whether a figure shows displacement or pressure before locating nodes.
Sources
- Physics (Giancoli)
- Physics (Cutnell and Johnson)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.