Tubo fechado harmônico n

fₙ = (2n−1)·v/(4L).
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

fₙ (Hz)
85,8 Hz

About this calculator

The Closed Tube Harmonic Calculator is an online tool that calculates the resonance frequency of a tube closed at one end and open at the other, also known as a harmonic tube. The formula used is fₙ = (2n−1)·v/(4L), where fₙ is the resonance frequency, n is the harmonic mode number, v is the speed of sound in the medium, and L is the length of the tube.

This calculator works based on the theory of sound waves in tubes. When a tube is closed at one end and open at the other, it can produce a series of resonance frequencies that are odd multiples of the fundamental frequency. The formula takes into account the harmonic mode number (n), the speed of sound (v), and the length of the tube (L) to calculate the resonance frequency.

The Closed Tube Harmonic Calculator is useful in various situations, such as in the design of musical instruments, analysis of ventilation systems, and in architectural acoustics applications. It is essential to remember that the speed of sound can vary depending on the medium and environmental conditions, which directly affects the result of the resonance frequency.

When using this calculator, it is crucial to be careful with the units of measurement and ensure that the input values are coherent and accurate. Additionally, it is important to consider the energy losses and end effects that may occur in real situations, but are not contemplated by the formula used.

Frequently asked questions

What is a harmonic tube?

A harmonic tube is a tube closed at one end and open at the other, capable of producing a series of resonance frequencies.

How does the formula fₙ = (2n−1)·v/(4L) work?

The formula calculates the resonance frequency based on the harmonic mode number, speed of sound, and length of the tube.

What are the units of measurement for the parameters?

The units of measurement are: Hz for frequency, m/s for speed of sound, and meters for tube length.

Can I use this calculator for any type of gas?

No, the calculator assumes the medium is air and that the speed of sound is constant. For other gases, the speed of sound may vary.

What are the limitations of the calculator?

The calculator does not take into account energy losses and end effects that may occur in real situations.

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