Enter the string/tube length, wave speed, and harmonic number to calculate the wavelength, frequency, node positions, and antinode positions of a standing wave. Choose between open-open, open-closed, or closed-closed boundary conditions to match your physical setup.
Resonant Frequency (fₙ)
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Wavelength (λₙ)
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Number of Nodes
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Number of Antinodes
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Fundamental Frequency (f₁)
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Period (T)
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A standing wave forms when two waves of identical frequency and amplitude travel in opposite directions through the same medium. Instead of propagating, the resulting wave pattern appears stationary, with fixed points of zero displacement called nodes and points of maximum displacement called antinodes.
A node is a point along the standing wave where the displacement is always zero — the medium does not move at that point. An antinode is a point of maximum oscillation, where the medium vibrates with the greatest amplitude. Nodes and antinodes alternate along the wave pattern.
The three key inputs are the length of the medium (L), the wave speed (v) in that medium, and the harmonic number (n). The boundary condition (open-open, closed-closed, or open-closed) also matters because it determines how wavelengths fit within the medium.
Open-open and closed-closed boundaries both support harmonics where λₙ = 2L/n, allowing all integer harmonics. An open-closed system only supports odd harmonics (n = 1, 3, 5…) with λₙ = 4L/n, because only a quarter-wavelength fits at the fundamental frequency.
The fundamental frequency (f₁) is the lowest resonant frequency of the system — also called the first harmonic. All higher resonant frequencies (overtones) are integer multiples of the fundamental for open-open and closed-closed systems, or odd multiples for open-closed systems.
Yes. For a vibrating string, enter the wave speed on the string (dependent on tension and linear density). For sound in a tube, use the speed of sound in air (~343 m/s at 20°C) and set the boundary condition to match whether the tube ends are open or closed.
For a given harmonic and boundary condition, nodes are spaced half a wavelength apart, and antinodes fall midway between consecutive nodes. This calculator displays all node and antinode positions in the results table, measured from the start of the medium.
The calculator uses the standard physics formulas for standing waves in ideal conditions. Real-world accuracy depends on how closely your physical setup matches the assumed ideal boundary conditions and uniform medium properties. For most educational and engineering estimation purposes, the results are highly reliable.