🚑 多普勒效应（声波）Doppler Effect Calculator

使用说明与常见问题How-to & FAQ

「多普勒效应（声波）」是什么？What is the Doppler Effect Calculator tool?

f′ = f (v + v₀) / (v - vₛ)：观察者靠近 v₀ 取正，声源靠近 vₛ 取正（远离为负）。本地处理。f′ = f (v + v₀) / (v - vₛ): observer speed v₀ positive when approaching, source speed vₛ positive when approaching (negative when receding). Processed locally.

如何使用「多普勒效应（声波）」？How do I use the Doppler Effect Calculator tool?

填写声源频率、声速、观察者速度和声源速度（相互靠近为正，远离为负），即可得到观察者听到的频率。结果会随输入实时更新。Enter the source frequency, the speed of sound and the observer and source speeds (positive when approaching, negative when moving apart) to get the frequency the observer hears. The result updates as you type.

光？Light?

光的多普勒效应需要相对论公式。Light needs the relativistic formula.

能举个计算实例吗？Can you show a worked example?

例如在「多普勒效应（声波）」中填 声源频率 Hz = 440，声速 m/s = 343，观察者速度 m/s（靠近为正） = 0，声源速度 m/s（靠近为正） = 20，结果区显示：观察到的频率：467.245 Hz；变化：+27.245 HzFor example, entering Source frequency Hz = 440, Speed of sound m/s = 343, Observer speed m/s (+ approaching) = 0, Source speed m/s (+ approaching) = 20 in the Doppler Effect Calculator gives: Observed frequency: 467.245 Hz; Shift: +27.245 Hz

哪些输入会被检查？Which inputs are validated?

「多普勒效应（声波）」会检查这些输入——「声源频率 Hz」、「声速 m/s」：必须填写，须大于 0；「观察者速度 m/s（靠近为正）」：必须填写，须为数字；「声源速度 m/s（靠近为正）」：必须填写，须为数字；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Doppler Effect Calculator checks its inputs — "Source frequency Hz", "Speed of sound m/s": required, must be greater than 0; "Observer speed m/s (+ approaching)": required, must be a number; "Source speed m/s (+ approaching)": required, must be a number; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「多普勒效应（声波）」的设置：「声源频率 Hz」默认 440；「声速 m/s」默认 343；「观察者速度 m/s（靠近为正）」默认 0；「声源速度 m/s（靠近为正）」默认 20。每次生成结果都按当前设置处理。Settings in the Doppler Effect Calculator — "Source frequency Hz" default 440; "Speed of sound m/s" default 343; "Observer speed m/s (+ approaching)" default 0; "Source speed m/s (+ approaching)" default 20. The result always uses the current settings.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「多普勒效应（声波）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Doppler Effect Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「多普勒效应（声波）」免费吗？需要注册吗？Is the Doppler Effect Calculator free? Do I need an account?

「多普勒效应（声波）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Doppler Effect Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.