Wave Calculator | Wavelength & Frequency
Calculate wavelength, frequency, period, and wave speed.
Solve For
Wave Speed Presets
What Is the Wave Calculator | Wavelength & Frequency?
The Wave Calculator solves all four wave properties simultaneously, wavelength (λ), frequency (f), wave speed (v), and period (T), plus angular frequency (ω), wave number (k), and photon energy for high-frequency EM waves. Choose any variable to solve for, enter two known values, and get the complete set of wave properties with SI-prefix formatting (MHz, nm, GHz, etc.). Built-in speed presets cover sound in air, water, and steel, plus the speed of light in vacuum and glass.
Formula
v = f × λT = 1 / fω = 2πfk = 2π / λE = h·fHow to Use
- ›Select what to solve for: Wavelength, Frequency, Wave Speed, or Period.
- ›Optionally click a Wave Speed Preset to auto-fill the medium (e.g. "Sound in air", "Light in vacuum").
- ›Enter the required inputs, only the relevant fields are shown based on your solve-for choice.
- ›Click Calculate to see all wave properties with SI prefix notation.
- ›For high-frequency EM waves (above 100 MHz), photon energy in eV is shown automatically.
Example Calculation
Example 1, Concert A note (440 Hz in air)
Example 2, Green light (550 nm)
Example 3, FM radio (98.5 MHz)
Understanding Wave | Wavelength & Frequency
The Wave Equation
All waves, mechanical or electromagnetic, obey the fundamental relation v = fλ. This equation links three independently observable quantities: the propagation speed of the wave in its medium, the number of oscillations per second, and the physical distance of one oscillation. A fourth property, period T = 1/f, describes how long one cycle takes.
- ›Wave speed is determined by the medium (air, water, glass, vacuum).
- ›Frequency is set by the source (speaker, antenna, laser).
- ›Wavelength is the result: λ = v/f.
Wave Speed Reference Table
| Medium | Wave type | Speed (m/s) | Notes |
|---|---|---|---|
| Air (20°C) | Sound | 343 | Increases ≈0.6 m/s per °C |
| Air (0°C) | Sound | 331 | Reference at freezing |
| Fresh water (25°C) | Sound | 1,497 | Warm freshwater |
| Sea water (25°C) | Sound | 1,531 | Higher salinity/density |
| Steel | Sound | 5,100 | Used in ultrasonic NDT |
| Vacuum | Light | 299,792,458 | c, exact by definition |
| Glass (n=1.5) | Light | 199,861,639 | v = c/n |
| Water (n=1.33) | Light | 225,407,863 | Causes refraction/rainbows |
| Optical fiber | Light | ~200,000,000 | Effective ≈ 0.67c |
EM Spectrum Classification
| Band | Frequency range | Wavelength | Photon energy | Applications |
|---|---|---|---|---|
| Radio | < 300 MHz | > 1 m | < 1.24 μeV | Broadcasting, WiFi |
| Microwave | 300 MHz–300 GHz | 1 m–1 mm | 1.24 μeV–1.24 meV | Radar, cooking, 5G |
| Infrared | 300 GHz–430 THz | 1 mm–700 nm | 1.24 meV–1.77 eV | Heat imaging, remote controls |
| Visible | 430–770 THz | 700–390 nm | 1.77–3.1 eV | Human vision |
| UV | 770 THz–30 PHz | 390–10 nm | 3.1–124 eV | Sterilization, lithography |
| X-ray | 30 PHz–30 EHz | 10–0.01 nm | 124 eV–124 keV | Medical imaging, crystallography |
| Gamma ray | > 30 EHz | < 0.01 nm | > 124 keV | Cancer therapy, astronomy |
Wave Properties in Context
- ›Angular frequency ω = 2πf, used in differential equations; the natural unit for oscillatory systems.
- ›Wave number k = 2π/λ, the spatial analogue of angular frequency; number of radians per metre.
- ›Wave equation, y(x,t) = A·sin(kx − ωt + φ) describes any sinusoidal wave completely.
- ›Dispersion, In dispersive media (glass, water surface), different frequencies travel at different speeds, causing pulse spreading and rainbows.
Frequently Asked Questions
What is the difference between frequency and wavelength?
Frequency (f) is the number of complete wave cycles per second (Hz). Wavelength (λ) is the physical distance between consecutive peaks or troughs. They are inversely related at constant wave speed: λ = v/f. High frequency means short wavelength; low frequency means long wavelength.
Why does sound travel faster in water than in air?
Sound speed depends on the medium's bulk modulus (resistance to compression) and density: v = √(B/ρ). Water is ~14,000× denser than air but ~15,000× stiffer, so the net effect is a higher sound speed (≈1,480 m/s in water vs. 343 m/s in air). Steel has an even higher speed (≈5,100 m/s) due to its extreme stiffness.
What is angular frequency and how is it different from frequency?
Ordinary frequency f counts cycles per second (Hz). Angular frequency ω = 2πf counts radians per second, it is the natural unit for oscillatory math because one full cycle = 2π radians. Angular frequency appears in all wave equations: y(x,t) = A·sin(kx − ωt).
What is photon energy and when does it matter?
Photon energy E = hf (where h = 4.136×10⁻¹⁵ eV·s is Planck's constant) describes the quantum of energy carried by an EM photon. This matters in optics, photochemistry, and medical imaging. Visible light photons carry 1.8–3.1 eV; X-ray photons carry 100 eV–100 keV, enough to ionize atoms.
What is the electromagnetic spectrum?
- ›Radio waves: f < 300 MHz, λ > 1 m
- ›Microwave: 300 MHz – 300 GHz
- ›Infrared: 300 GHz – 430 THz
- ›Visible light: 430–770 THz (700–390 nm)
- ›Ultraviolet: 770 THz – 30 PHz
- ›X-ray: 30 PHz – 30 EHz
- ›Gamma ray: f > 30 EHz