# 驻波可视化 - Standing Wave

由入射波和反射波形成的驻波交互式模拟

> 标准页面: https://elysiatools.com/zh/visualizations/standing-wave

- **分类:** Physics

## 概述

Interactive standing wave simulation showing nodes, antinodes, and harmonic frequencies. Features standing wave equations: y₁ = Asin(kx - ωt) (incident wave), y₂ = Asin(kx + ωt) (reflected wave), y = y₁ + y₂ = 2Asin(kx)cos(ωt) (standing wave). Nodes occur at sin(kx) = 0 → x = nλ/2 (zero displacement points), antinodes at |sin(kx)| = 1 → x = (2n+1)λ/4 (maximum amplitude points). Real-time visualization of three wave displays: Incident wave (blue) traveling right, Reflected wave (red) traveling left, and Standing wave (purple) showing the superposition with envelope. Split-screen display shows how incident and reflected waves combine to form standing wave pattern. Adjustable parameters: string length L (0.5-5.0 m), harmonic number n (1-10), frequency f (0.1-10 Hz), amplitude A (0.1-2.0), wave speed v (0.5-5.0 m/s), and animation speed. Harmonic presets for fundamental (1st), 2nd, 3rd, 4th, and 5th harmonics. Display options include show nodes (green markers), show antinodes (orange markers), show envelope, and resolution control. Real-time statistics display node count, antinode count, and wavelength λ = v/f. Applications in musical instruments (guitar strings, wind instruments, organ pipes) demonstrating resonance and harmonics; string vibration physics; acoustics and room modes; quantum mechanics (particle in a box as standing matter wave); and architectural acoustics. Multi-language support (zh, en, es, fr, de, ru, pt).

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