๐บ Pipe Resonance Calculator
Open pipe: f = v/(2L). Closed pipe: f = v/(4L). Speed of sound is calculated from temperature.
Enter a pipe's length and the air temperature to calculate the fundamental frequency produced by resonance in an open pipe (open at both ends) or a closed pipe (closed at one end). You can also work backward from a target frequency to find the required pipe length.
How to use
- Select "Length to frequency" or "Frequency to length".
- Select open or closed pipe.
- Enter the pipe length (or frequency) and air temperature.
- The result is calculated automatically.
How the calculation works
This tool relates the length of a pipe to the pitch (fundamental) produced by the air resonating inside it. Find the frequency from the length or the length needed for a frequency. Open pipe (both ends open): f = v รท (2L) Closed pipe (one end closed): f = v รท (4L) (v: speed of sound, L: pipe length) The speed of sound is calculated from temperature as 331.3 ร โ(1 + temperature รท 273.15) m/s. For the same length, a closed pipe sounds an octave lower than an open one. Flutes and recorders behave as open pipes; clarinets and blowing across a bottle behave like closed pipes.
Worked example
Length 0.5 m at 20ยฐC Open: 343.2 รท (2 ร 0.5) โ 343.2 Hz Closed: 343.2 รท (4 ร 0.5) โ 171.6 Hz Open pipe length for 440 Hz (A4) 343.2 รท (2 ร 440) โ 0.390 m (about 39 cm)
Things to be aware of
- In real pipes the air vibrates slightly beyond an open end, so the pitch is a little lower by the โend correctionโ (about 0.6 times the pipe radius).
- Warmer air raises the speed of sound and so the pitch of wind instruments, which is why players warm up their instruments before tuning.
- Closed pipes produce only odd harmonics (3ร, 5รโฆ), which gives the clarinet its characteristic tone.
FAQ
Whatโs the difference between an open and closed pipe?
An open pipe has both ends open (like a recorder), while a closed pipe has one end closed (like blowing across a bottle opening). For the same length, a closed pipe sounds exactly one octave lower than an open pipe.
Whatโs the formula?
An open pipeโs fundamental frequency is f = v/(2L), and a closed pipeโs is f = v/(4L), where v is the speed of sound (temperature-dependent) and L is the pipe length. The speed of sound is 331.3 ร โ(1 + temperature (ยฐC) รท 273.15) m/s.
Does temperature affect the result?
Yes. The speed of sound increases with temperature, so a pipe of the same length produces a slightly higher frequency at a higher temperature.