Wavenumber Calculator
Calculate wavenumber and angular wavenumber from wavelength or frequency
Calculate Wavenumber
The distance between two consecutive peaks or troughs of a wave
Wavenumber Results
Wave Properties
Electromagnetic Spectrum
Formulas used: k = 1/λ, k = 2π/λ
Units: Wavenumber (m⁻¹), Angular wavenumber (rad/m)
Spectrum Analysis
Example Calculation
Yellow Light Example
Wavelength: 580 nm (yellow light)
Convert to meters: 580 × 10⁻⁹ m = 5.8 × 10⁻⁷ m
Wavenumber Calculation
k = 1/λ = 1/(5.8 × 10⁻⁷ m)
k = 1.724 × 10⁶ m⁻¹
Angular wavenumber = 2π × 1.724 × 10⁶
k = 1.083 × 10⁷ rad/m
Wavenumber Quick Reference
Wavenumber (k)
k = 1/λ
Number of wavelengths per unit distance
Angular Wavenumber
k = 2π/λ
Number of radians per unit distance
From Frequency
k = f/v
Using wave equation v = fλ
Units & Constants
Wavenumber Units
m⁻¹ (inverse meters)
Angular Wavenumber Units
rad/m (radians per meter)
Speed of Light
c = 299,792,458 m/s
Common Conversions
- 1 nm = 10⁻⁹ m
- 1 µm = 10⁻⁶ m
- 1 cm⁻¹ = 100 m⁻¹
Applications
Spectroscopy
IR and Raman spectroscopy use wavenumbers
Quantum Mechanics
Wave vector in quantum wave functions
Crystallography
Reciprocal lattice calculations
Wave Physics
Describing wave propagation
Understanding Wavenumber
What is Wavenumber?
Wavenumber is a fundamental concept in wave physics that describes the spatial frequency of a wave. It represents the number of wave cycles that occur over a unit distance, typically measured in inverse meters (m⁻¹).
Types of Wavenumber
- •Wavenumber (k): k = 1/λ, measured in m⁻¹
- •Angular wavenumber: k = 2π/λ, measured in rad/m
- •Spectroscopic wavenumber: Often in cm⁻¹ units
Key Relationships
Basic Wavenumber
k = 1/λ
Inverse of wavelength
Angular Wavenumber
k = 2π/λ
For quantum mechanics
From Frequency
k = f/v = 2πf/v
Using wave equation
Applications in Physics
Spectroscopy
Infrared and Raman spectroscopy commonly use wavenumbers (cm⁻¹) to characterize molecular vibrations and identify chemical compounds.
Quantum Mechanics
The wave vector k in quantum mechanics describes particle momentum through the de Broglie relation p = ℏk, where ℏ is the reduced Planck constant.
Crystallography
Reciprocal lattice vectors in crystallography are expressed as wavenumbers, essential for X-ray diffraction and structure determination.