\[c = \lambda\nu,\qquad \tilde\nu = \frac1\lambda = \frac\nu c\]
含义Meaning
电磁波的传播速度等于波长乘频率。光谱学常用波数（cm⁻¹），它与能量成正比。
An electromagnetic wave travels at wavelength × frequency. Spectroscopy often uses wavenumber (cm⁻¹), which is proportional to energy.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(c\) | 真空光速 2.998×10⁸ m/sspeed of light in vacuum | m·s⁻¹ |
| \(\lambda\) | 波长wavelength | m |
| \(\nu\) | 频率frequency | Hz |
| \(\tilde\nu\) | 波数wavenumber | cm⁻¹ |
推导Derivation
一个周期 1/ν 内波前进一个波长 λ，所以速度 = λ/(1/ν)。
In one period 1/ν the wave advances one wavelength.
波数定义为单位长度内的波数目。
Wavenumber counts waves per unit length.
适用条件与局限Assumptions & limitations
介质中光速 c/n 变小、波长变短，频率不变。
In a medium speed and wavelength shrink by n; frequency is unchanged.
例题Worked example
钠黄光 589 nm：ν = 5.09×10¹⁴ Hz，ν̃ = 16 978 cm⁻¹。
Sodium D line 589 nm: 5.09×10¹⁴ Hz, 16 978 cm⁻¹.