Tubo aberto harmônico n
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
This calculator determines the nth harmonic frequency in an open tube using the formula fₙ = n·v/(2L). Open tubes with both ends free generate standing waves with antinodes at the edges, producing integer harmonics. The speed of sound (v) and tube length (L) are key factors in the calculation.
To use it, input the speed of sound in the medium (typically 343 m/s in air at 20°C), the tube length, and the desired harmonic number (n ≥ 1). The calculation multiplies n by the speed and divides by twice the length. This reflects the wave pattern in open tubes, where each harmonic is an integer multiple of the fundamental frequency.
This tool is valuable in acoustics, musical instruments (e.g., flutes), and vibration studies. For example, a 0.5 m tube with n = 2 and v = 343 m/s gives f₂ = 2·343/(2·0.5) = 686 Hz. Note: the speed of sound varies with temperature and material, affecting results.
Precautions: use consistent units (meters, seconds), and remember open tubes only have even harmonics (n = 1, 2, 3...). In humid or high-pressure environments, adjust v using specific sound speed tables.
Frequently asked questions
How does the formula fₙ = n·v/(2L) relate to open tubes?
This formula calculates standing wave frequencies in open tubes where n = 1, 2, 3... indicates the harmonic number. The 2L denominator reflects that nodes are at the ends, requiring the tube length to be half the wavelength.
Why does sound speed vary with temperature?
Sound speed in air increases with temperature because molecules move faster. The approximation v = 331 + 0.6·T (°C) is commonly used for dry air calculations.
Can this calculator be used for closed tubes?
No. Closed tubes use fₙ = (2n-1)·v/(4L), producing only odd harmonics. This tool is exclusive to open tubes.
What happens if I input a non-integer harmonic number?
The calculator accepts decimals but physical harmonics require n as a positive integer. Decimal results are theoretical and not reproducible in real-world instruments.
Why do flutes use open tubes?
Flutes and other wind instruments with open ends produce a full range of harmonics, allowing greater control over pitch and timbre compared to closed tubes.