Organ Pipes
Simple Explanation
Organ pipes produce sound via resonating air columns, and come in two types: closed pipes (closed at one end, like the resonance column) and open pipes (open at both ends). An open pipe's fundamental frequency occurs when its length equals half the sound wavelength (L = Ξ»/2).
Why Do We Need It?
Comparing open and closed pipes reveals how boundary conditions (open vs. closed ends) shape which frequencies a resonating air column can produce, a principle used in the design of real musical wind instruments.
Formula
Fundamental Frequency of an Open Pipe
f = v / 2L
A pipe open at both ends produces its fundamental (lowest) frequency when its length equals half the sound wavelength.
- f
- β Fundamental frequency, in Hz
- v
- β Speed of sound in air, in m/s
- L
- β Length of the pipe, in metres
When to use it: Use to find the fundamental frequency (or required length) of an organ pipe open at both ends.
Worked Example
Finding the fundamental frequency of an open pipe
An organ pipe open at both ends is 1.2 m long. Find its fundamental frequency (speed of sound = 340 m/s).
Why Does This Work?
Both ends of an open pipe are free to move (antinodes), so the shortest air column pattern that fits an antinode at each end (with one node in the middle) spans exactly half a wavelength β this is different from a closed pipe (node at one end, antinode at the other), which needs only a quarter wavelength for its shortest resonant pattern.
Real-Life Example
Why open and closed organ pipes of the same length sound different
A closed pipe and an open pipe of the same physical length produce different musical pitches.
Because closed pipes resonate at L = Ξ»/4 (needing only a quarter wavelength) while open pipes need L = Ξ»/2 (half a wavelength) for the fundamental, a closed pipe of a given length produces exactly half the fundamental frequency of an open pipe of the same length β a full octave lower.
Practice
An open organ pipe has a fundamental frequency of 200 Hz. Find its length (v = 340 m/s).
MediumCommon mistake
Using the closed-pipe formula (L = Ξ»/4) for an open pipe, or vice versa β always check the boundary conditions (open = antinode, closed = node) before choosing which relationship applies.
Quick Review
- Open pipes: antinode at both ends, fundamental at L = Ξ»/2 (f = v/2L).
- Closed pipes: node at closed end, antinode at open end, fundamental at L = Ξ»/4.
- A closed pipe produces a fundamental one octave lower than an open pipe of the same length.