Wavelength and Frequency Calculator
Convert wavelength to frequency with f = v / λ, find wavelength with λ = v / f, or solve wave speed with v = fλ. Choose the medium before entering your values.
Wave Mechanics Parameters
v = f · λ
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How to convert wavelength to frequency
- Choose the medium. Use 299,792,458 m/s for light in vacuum; sound in air uses a much lower speed that depends on temperature.
- Select the quantity to solve and enter the two known values. Set the units beside each input: 1 nm = 10⁻⁹ m and 1 THz = 10¹² Hz.
- Read the result. At a fixed wave speed, doubling frequency halves wavelength.
Example: 620 nm light in vacuum
f = 299,792,458 / (620 × 10⁻⁹) ≈ 4.83536 × 10¹⁴ Hz, or 483.536 THz. Enter 620 and select nm; using 620 m would give a completely different result.
See the 620 nm color approximationExample: a 440 Hz tone in air
Using this calculator's 20°C air preset, λ = 343.21 / 440 ≈ 0.780 m, or 78.0 cm. The frequency is the same A4 reference used in music; its wavelength changes when the propagation speed changes.
Play the A4 reference toneWant to see the relationship? Open the harmonic wave simulator to vary amplitude, frequency and wavelength. For the underlying model, see OpenStax on wave properties.
Live Wave Propagation Simulator
Observe the dynamic relationship between wavelength (spatial cycle), frequency (temporal rate), and wave speed.
Harmonic Sine Wave Simulation
y(x, t) = A · sin(2π(x/λ - f·t))
1. Mathematical Derivation of the Universal Wave Equation
A periodic wave is an oscillation propagating through space over time. In a single oscillation period T, one full spatial wave cycle of length λ (wavelength) travels a distance equal to its wavelength. By standard kinematic definition, speed equals distance divided by time:
Since frequency is the reciprocal of the temporal period (f = 1/T), multiplying frequency by wavelength yields the wave propagation velocity v.
Wave Velocity (m/s): The speed at which wave phase fronts travel through the transmission medium.
Frequency (Hz): Number of full wave crests passing a fixed spatial coordinate per second.
Wavelength (m): The physical spatial distance between two consecutive identical points of phase (e.g. crest-to-crest).
2. Wave Speed Across Physical Media (Electromagnetic vs. Acoustic)
While electromagnetic waves (light) achieve maximum velocity in a vacuum and slow down in dense matter, mechanical waves (sound) require matter to propagate and travel faster in dense, stiff solids:
| Medium | Wave Nature | Propagation Speed (v) | λ at 1,000 Hz | Governing Physical Law |
|---|---|---|---|---|
| Vacuum | Light (EM) | 299,792,458 m/s | 299.79 km | Maxwell Equations (c = 1 / √ε₀μ₀) |
| Air (20°C, 1 atm) | Sound (Acoustic) | 343.21 m/s | 34.32 cm | Ideal Gas Laplace (v = √γRT / M) |
| Fresh Water (20°C) | Sound (Acoustic) | 1,482 m/s | 1.48 m | Bulk Modulus (v = √K / ρ) |
| Pure Water (20°C) | Light (EM) | 224,900,568 m/s | 224.90 km | Refractive Index (v = c / n) |
| Structural Steel | Sound (Acoustic) | 5,960 m/s | 5.96 m | Young Modulus (v = √E / ρ) |
Explore Electromagnetic Waves in Light Lab
Investigate the 380 nm – 750 nm visible spectrum, convert nanometers to exact RGB chromaticities, and explore photon energies across the optical spectrum.
Launch Light Lab (371 Spectral Wavelengths)Explore Acoustic Waves in Sound Lab
Calculate musical pitch frequencies across all 88 piano keys, compute room acoustic wavelengths, and evaluate the thermodynamic speed of sound in air.
Launch Sound Lab (88 Piano Keys & Tuning)Frequently Asked Physics Questions
What is the universal wave equation?
The universal wave equation relates the propagation speed of a wave (v) to its frequency (f) and wavelength (λ): v = f · λ. This relationship holds universally for all periodic harmonic waves, including electromagnetic radiation (light, radio, X-rays), mechanical sound waves, water waves, and seismic disturbances.
Why does wave frequency remain constant when entering a different medium?
Frequency is determined exclusively by the wave source's oscillation rate. When a wave crosses a boundary into a medium with different optical or acoustic density, its propagation velocity changes. To satisfy v = f · λ, the wavelength (λ) compresses or expands proportionally while frequency (f) remains invariant.
How do you calculate photon energy from wavelength or frequency?
For electromagnetic waves in quantum mechanics, photon energy is calculated using the Planck-Einstein relation: E = h · f = (h · c) / λ, where h is the Planck constant (6.62607015 × 10⁻³⁴ J·s) and c is the speed of light in vacuum (299,792,458 m/s).