Flute Pipe Length for Frequency Calculator

Open-open flute tube length from frequency: formula and example

In an ideal cylindrical pipe open at both ends, the fundamental frequency works out to f = v / (2L), which rearranges to L = v / (2f). Take the speed of sound as v ≈ 343 m/s at 20 °C. Then C5 (523 Hz) needs L ≈ 0.328 m (~33 cm), A4 (440 Hz) lands near 39 cm, and C4 (262 Hz) around 65 cm. Real flutes come out a touch shorter because of the end correction (~0.6 × bore radius at each open end).

Context and applications

Luthiers building transverse flutes, recorders, or the Brazilian Northeastern pífaro (often PVC or bamboo) rely on this to place the open end and the embouchure hole. When you overblow into the second harmonic, the frequency doubles, an octave up, because you've excited the n=2 mode without touching the tube length. The cross-section and wall material color the timbre, though they nudge the pitch only slightly.

FAQ

Why divide by 2L? A tube open at both ends holds standing waves with antinodes at each end. The longest one fits a single half-wavelength inside L, which gives λ = 2L and f = v/λ.

How much does temperature matter? Quite a bit: v ≈ 331.3 + 0.606·T(°C) m/s. Going from 15 °C to 30 °C, v climbs about 9 m/s, which lifts the pitch roughly 2.5%. That's why wind instruments sharpen as the player warms them up.

What about finger holes? Open a hole and the acoustic length effectively shrinks down to that hole, give or take a small correction. So the formula describes the lowest note, with every hole closed. Higher notes call for a shorter effective L.