# 多普勒效应 - Doppler Effect

由于相对运动引起波的频率变化的交互式模拟

> 标准页面: https://elysiatools.com/zh/visualizations/doppler-effect

- **分类:** Physics

## 概述

Interactive Doppler effect simulation demonstrating wave frequency changes due to relative motion between source and observer. Features Doppler formulas: f' = f₀·(v + vᵣ)/(v + vₛ) (general), f' = f₀·v/(v ± vₛ) (source motion), f' = f₀·(v ± vᵣ)/v (observer motion), where v = 343 m/s (speed of sound). Visual display includes wave source (S) and observer (O) on a 2D plane, animated wavefronts showing compression (blue, approaching) and rarefaction (red, receding), velocity vectors with magnitude labels, real-time frequency statistics (source frequency f₀, observed frequency f', frequency change Δf, ratio change %), and waveform comparison chart showing source vs observed waves. Adjustable parameters: source frequency f₀ (100-1000 Hz), source velocity vₛ (-150 to 150 m/s), source position xₛ, observer velocity vᵣ (-150 to 150 m/s), observer position xᵣ, wave speed v (100-500 m/s), wave amplitude, and animation speed. Scenario presets for stationary both, source approaching, source receding, observer approaching, and high speed source (supersonic effects). Display options include show/hide wavefronts, Doppler color map (blue/red gradient), and velocity vectors. Color coding: blue shift = higher frequency (approaching), red shift = lower frequency (receding). Applications in astronomy (redshift/blueshift for stellar velocities), radar speed detection, medical ultrasound Doppler imaging, emergency vehicle sirens, weather radar for wind patterns, and laser cooling in quantum physics. Multi-language support (zh, en, es, fr, de, ru, pt).

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