Onda Estacionária (nós)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
λ_n = 2L/n
About this calculator
The standing wave (nodes) calculator determines the wavelength of harmonics on a string fixed at both ends. The formula used is λ_n = 2L/n, where L is the string length and n is the harmonic number (n = 1, 2, 3...). The result shows the nodal points where amplitude is zero. This tool is useful for physics and engineering students studying standing waves in string musical instruments.
To use the calculator, enter the string length in meters and the desired harmonic number. The calculation is instant and provides the corresponding wavelength. Remember that the formula applies only to strings fixed at both ends, like those of guitars or pianos. If the string has a free end, the relationship changes to λ_n = 4L/n.
When to use this calculator? In practical situations such as designing musical instrument strings, analyzing vibration frequencies in cables, or studying resonance in physics labs. For example, when adjusting the tension of a guitar string to obtain a specific note, the wavelength of the fundamental harmonic (n=1) determines the frequency.
Important precautions: the formula assumes an ideal string, without stiffness or damping. In practice, string stiffness can slightly alter the wavelengths. Also, the harmonic n must be a positive integer. Non-integer or negative values do not produce stable standing waves.
Frequently asked questions
What does n mean in the formula?
n is the harmonic number, a positive integer (1, 2, 3...). n=1 is the fundamental harmonic, n=2 the first overtone, etc.
Can I use this calculator for strings with one free end?
No. For strings with one free end, the formula is λ_n = 4L/n. This calculator is only for strings fixed at both ends.
Does wavelength influence frequency?
Yes. Frequency f is given by f = v/λ, where v is the wave speed on the string. Smaller wavelength means higher frequency.
What are nodes in a standing wave?
Nodes are points on the string where the amplitude is always zero. On a fixed string, the ends are nodes. For harmonic n, there are n+1 nodes.
Does the calculator work for strings of different materials?
Yes, as long as the string is fixed at both ends. The formula is independent of material, but wave speed depends on tension and linear density.