Standing Wave API

Standing-wave and resonance maths for strings and air columns as an API, computed locally and deterministically. The string endpoint models a string fixed at both ends: from its length and the wave speed — given directly or as the tension and the linear mass density (which you can supply directly, or have computed from a mass and length, or from a wire diameter and material density) — it returns the wave speed v = √(T/μ), the fundamental frequency f₁ = v/(2L) and the harmonic series f_n = n·f₁, each with its wavelength and node and antinode count; it can also solve the tension needed to tune the string to a target fundamental. The pipe endpoint does the same for an air column: an open pipe (both ends open) resonates at all harmonics f_n = n·v/(2L) while a closed (stopped) pipe resonates only at the odd harmonics f_n = (2n−1)·v/(4L), with the speed of sound given directly or worked out from the air temperature, v = 331.3·√(1 + θ/273.15). The harmonics endpoint generates the harmonic series from a fundamental frequency, or from a wave speed and a length, for a string, an open pipe or a closed pipe. Everything is computed locally and deterministically, so it is instant and private. Ideal for musical-instrument and luthier tools, acoustics and audio apps, organ-pipe and wind-instrument design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is mechanical standing waves and resonance; for note-to-frequency music theory use a music-note API and for electromagnetic wavelength λ = c/f use a wavelength API.