Standing waves calculator: vibrating strings and air columns

How to use (3 steps)

Pick the system: vibrating string or air column (open–open / open–closed).
Enter length and either tension & density or sound speed (or temperature for tubes). Leave the example values if you just want to see a demo.
Tap Compute. The mode table, fundamental, and step-by-step formulas update instantly. Copy URL shares the exact setup.

Key formulas: string fₙ = n·v/(2L); open–open tube fₙ = n·v/(2L); open–closed tube fₙ = (2n−1)·v/(4L).

Inputs

Number of modes

Vibrating string (both ends fixed) Air column (tube)

String inputs

String length L m

How to specify wave speed

Use tension T and linear density μ (v = √(T/μ)) Enter wave speed v directly

Tension T N

Linear density μ kg/m

Wave speed v m/s

Results

Fundamental and mode table update when you press Compute or change the mode settings. For open–closed tubes, only odd harmonics (1st, 3rd, 5th, …) appear.

How it is calculated

FAQ

What assumptions does this standing wave calculator use?

It assumes ideal strings and tubes with no losses or end correction. Use it for quick estimates and intuition.

Why might real instruments sound different from these results?

Real instruments have stiffness, damping, air viscosity, and end correction that shift resonance. Expect differences from ideal formulas.

How does temperature affect tube resonance?

Sound speed in air is approximated by v ≈ 331 + 0.6·T (°C). Warmer air increases sound speed and raises the resonant frequencies.

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Standing waves calculator (strings & tubes)