7-Hole Flute Acoustics Worksheet Acoustics Lab

Pipe Lengths, Speed of Sound & End Correction Calculator

inches

Internal diameter of flute body tube.

in/sec

Standard 13,622 in/s ≈ 346 m/s at 24.5°C (76°F).

Quickly load standard musical scales.

Toggles formulas and display units.

Western Modes: Blues & Pentatonic: Tri, Tetra, Hexa, Octa & EDO:

Hole Frequencies & Notes

7 Tone Holes
Hole Note Frequency (Hz) Play
Acoustic End Correction Physics

Sound waves extend slightly past the physical opening of a pipe before reflecting. For an un-flanged open tube end or tone hole, the standard acoustic end correction is:

ΔL = 0.6 × R

where R is the internal bore radius (R = Bore Diameter / 2).

ACOUSTICS FORMULA WORKSHEET

7-HOLE FLUTE PIPE LENGTHS

Formula: L = (v / 2f) - 0.6R

Speed of Sound (v): 13622 in/s
Bore Radius (R): 0.375 in
End Correction (0.6R): 0.225 in

Calculated acoustic values for each note (Step 1: Raw Length; Step 2: Final Corrected Length):

Cut Length Summary Table

Hole # Note Freq (Hz) Raw Pipe Length End Correction Final Pipe Length
Flute Craft / Maker: ____________________
Date: ____________________

Acoustic Tube & Hole Position Diagram

Visual scale representation of calculated physical length from embouchure / stopper to open tone holes.

Total Tube Fundamental Length: 0.00 in
Stopper / Embouchure: Reference zero point (0.00)
Tone Holes 1 - 7: Uncovered lengths
End Correction (0.6R): Subtracted acoustic shift

Flute Acoustics & Calculation Guide

1. Half-Wavelength Physics

An open cylindrical pipe vibrates at half-wavelength fundamentals ($\lambda / 2$). The uncorrected acoustic wave length $L_0$ for a frequency $f$ and speed of sound $v$ is given by:

L₀ = v / (2 × f)

2. End Correction (0.6R)

The standing wave inside the flute extends slightly beyond the physical opening into surrounding ambient air. To tune the note accurately, this virtual extension $0.6 \times R$ is subtracted:

L_final = L₀ - 0.6R

3. Temperature Impact

Speed of sound in dry air varies with temperature $T$ (°C):

v ≈ 331.3 × √(1 + T / 273.15) m/s

At room temperature (20°C / 68°F), $v \approx 13,504\text{ in/s}$. At warm breath temperature (24.5°C / 76°F), $v \approx 13,622\text{ in/s}$.