How to use the vibrating string frequency calculator
Find the fundamental frequency of a stretched string. Enter length, tension, linear density in the fields above; the wave speed, fundamental frequency, second harmonic, third harmonic are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- L — Length (m)
- T — Tension (N)
- mu — Linear density (g/m)
Worked example
With length = 0.65 m, tension = 70 N, linear density = 0.4 g/m, the calculator gives wave speed ≈ 418.33 m/s; fundamental frequency ≈ 321.7923 Hz; second harmonic ≈ 643.5846 Hz; third harmonic ≈ 965.377 Hz.
Frequently asked questions
What is the formula for the vibrating string frequency calculation?
Wave speed (m/s) = √(T / (mu / 1000)). Fundamental frequency (Hz) = [Wave speed] / (2 × L). Second harmonic (Hz) = 2 × [Fundamental frequency]. Third harmonic (Hz) = 3 × [Fundamental frequency]. Here L is length (m), T is tension (N), mu is linear density (g/m).
What inputs do I need for the vibrating string frequency calculator?
You need length in m, tension in N, linear density in g/m. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.