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01 // 图表工作室02 // 可视化求解器03 // 双向计算器04 // 公式百科05 // Unicode 与开发
03 // 双向 STEM 与金融计算器 // 物理力学、电磁学与热力学计算器f_obs = f_src × (c / (c - v_src))

多普勒效应频率偏移计算器

求解观察者接收到的多普勒频移频率、波源发射频率、波源移动速度或观察者速度。

f_obs = f_src × (c / (c - v_src))
选择要计算的未知量（或直接在任意输入框中输入数值）：当前求解: f_obs — Observed Frequency
计算结果

Apparent pitch or frequency measured by stationary observer

11.0000e+9

True rest frequency emitted by the moving source

11.0000e+9

Velocity of source toward observer (+ approaching, - receding)

-300300

Propagation velocity in the medium (343 m/s for air)

50300,000,000.00
计算结果 · Observed Frequency (f_obs)
762.2222Hz
单位换算：

分步代入计算过程

01Canonical Law: f_obs = f_src × (c / (c - v_src))
02Given Inputs (Base Units): f_src = 700 Hz, v_src = 28 m/s, c = 343 m/s
03Solve for f_obs (Observed Frequency): f_obs = 762.22 Hz

The classical Doppler Effect calculates the apparent shift in wave frequency f_obs when a source moving at velocity v_src approaches an observer in a medium of wave speed c: f_obs = f_src × c / (c - v_src).

常见参考标准值

Ambulance Siren @ 100 km/h (27.8 m/s)+8.8% Pitch Shift Approaching

Drops -7.5% below rest pitch once receding

Mach 1 Sonic Boom Limitv_src → c (343 m/s)

Wavefronts pile up into a Mach shock cone

Doppler Weather & Traffic RadarΔf = 2 v f₀ / c

Two-way reflection doubles the frequency shift

20 行数值对照表

Observed Frequency (f_obs) · Source Emitted Frequency (f_src)

Doppler Effect Frequency Shift Calculator — Source Emitted Frequency → Observed Frequency
#Source Emitted Frequency (Hz)Observed Frequency (Hz)Δ %
01700 Hz当前762.2222 Hz0.00%
027,236,879.89 Hz7,880,158.10 Hz+1033739.98%
0314,473,758.78 Hz15,760,315.11 Hz+2067579.83%
0421,710,637.66 Hz23,640,472.12 Hz+3101419.67%
0528,947,516.55 Hz31,520,629.13 Hz+4135259.51%
0636,184,395.44 Hz39,400,786.14 Hz+5169099.35%
0743,421,274.33 Hz47,280,943.15 Hz+6202939.19%
0850,658,153.21 Hz55,161,100.16 Hz+7236779.03%
0957,895,032.10 Hz63,041,257.18 Hz+8270618.87%
1065,131,910.99 Hz70,921,414.19 Hz+9304458.71%
1172,368,789.88 Hz78,801,571.20 Hz+10338298.55%
1279,605,668.76 Hz86,681,728.21 Hz+11372138.39%
1386,842,547.65 Hz94,561,885.22 Hz+12405978.24%
1494,079,426.54 Hz102,442,042.23 Hz+13439818.08%
15101,316,305.43 Hz110,322,199.24 Hz+14473657.92%
16108,553,184.31 Hz118,202,356.25 Hz+15507497.76%
17115,790,063.20 Hz126,082,513.26 Hz+16541337.60%
18123,026,942.09 Hz133,962,670.27 Hz+17575177.44%
19130,263,820.98 Hz141,842,827.28 Hz+18609017.28%
20137,500,699.86 Hz149,722,984.29 Hz+19642857.12%
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常见问题解答 (FAQ)

如何使用在线 多普勒效应频率偏移计算器 工具？+

输入已知参数或拖动滑块，即可在浏览器中实时计算并可视化 多普勒效应频率偏移计算器（基于关系式 f_obs = f_src × (c / (c - v_src))）。求解观察者接收到的多普勒频移频率、波源发射频率、波源移动速度或观察者速度。

可以导出或打印 多普勒效应频率偏移计算器 的结果吗？+

可以。支持一键复制数据、打印计算工作表或导出高清 SVG、PNG 和 CSV 文件。

我可以清空 多普勒效应频率偏移计算器 中的示例数据并从空白状态开始吗？+

可以。点击工具顶部的“清空 / 空白开始”按钮即可重置所有输入项，随时也可一键重新加载示例数据。