Wavelength Frequency Calculator
Wavelength (m)
300
Period (μs)
1
How it works
Wavelength (λ) and frequency (f) are related by the wave equation: λ = v/f, where v is wave propagation speed. For electromagnetic waves in vacuum: v = c = 2.998 × 10⁸ m/s. For sound in air at 20°C: v ≈ 343 m/s.
**EM spectrum by wavelength and frequency** AM radio: 550–1600 kHz (wavelength: 200–545 m). FM radio: 87.5–108 MHz (wavelength: 2.8–3.4 m). Wi-Fi 2.4 GHz (wavelength: 12.5 cm). 5G Sub-6 GHz (wavelength: 5–10 cm). 5G mmWave: 24–100 GHz (wavelength: 3–12 mm). Visible light: 400–700 nm (430–750 THz). X-rays: 0.01–10 nm. Gamma rays: < 0.01 nm.
**Sound wavelengths** 20 Hz (lowest audible): wavelength = 343/20 = 17 m. 1 kHz (speech fundamental): wavelength = 0.34 m. 20 kHz (upper hearing limit): wavelength = 17 mm. Ultrasound at 2 MHz (medical imaging): 0.77 mm. Wavelength determines diffraction and absorption behavior — low-frequency sound diffracts around buildings; high frequencies are blocked and absorbed.
**Photon energy** For electromagnetic radiation: E = h × f = h × c / λ, where h is Planck's constant (6.626 × 10⁻³⁴ J·s). Higher frequency = shorter wavelength = higher photon energy. UV photons have enough energy to break chemical bonds (causing sunburn). X-ray and gamma photons ionize atoms — why they're dangerous in high doses and useful for medical imaging.
**Doppler effect** When source and observer are in relative motion, observed frequency f_obs = f_source × (v ± v_observer) / (v ∓ v_source). Approaching: frequency increases (blueshift). Receding: frequency decreases (redshift). Radar guns, weather radar, and medical ultrasound all use Doppler shift to measure velocity.
Frequently Asked Questions
- f = c / λ, where c = 2.998 × 10⁸ m/s. Red light (700 nm): f = 2.998×10⁸ / 700×10⁻⁹ = 4.28 × 10¹⁴ Hz = 428 THz. Violet light (400 nm): f = 7.50 × 10¹⁴ Hz = 750 THz. The visible spectrum spans 400–700 nm (750–430 THz). Note that wavelength changes when light enters a medium with different refractive index (λ_medium = λ_vacuum / n), but frequency stays constant. This is why a lens bends light — the wavelength (and thus speed) changes, but frequency is preserved.
- Speed of sound: v = √(γ × P / ρ) = √(γRT/M) for ideal gas, where γ is heat capacity ratio, R is gas constant, T is absolute temperature, M is molar mass. For air at 20°C (293 K): v = √(1.4 × 8.314 × 293 / 0.029) = 343 m/s. At 0°C: v = 331 m/s (√20 factor slower). In water: ~1480 m/s (much stiffer medium). In steel: ~5000 m/s. Speed increases with temperature because higher temperature → faster molecular motion → faster pressure pulse propagation. This is why concert halls have different acoustic behavior at different temperatures.
- E = hf = hc/λ, where h = 6.626×10⁻³⁴ J·s (Planck's constant). Visible light photons: red (700 nm): E = 6.626×10⁻³⁴ × 2.998×10⁸ / 700×10⁻⁹ = 2.84×10⁻¹⁹ J = 1.77 eV. UV at 300 nm: 4.1 eV — enough to break C-C chemical bonds and cause DNA damage (sunburn). X-ray at 0.1 nm: 12,400 eV = 12.4 keV — enough to ionize atoms. The threshold for photoelectric effect (Einstein's Nobel Prize discovery): photons below a threshold frequency cannot eject electrons regardless of intensity — only photons above the threshold have enough energy per photon.
- Radar resolution (minimum target separation) ≈ λ/2 in range for pulse compression systems. L-band (1–2 GHz, λ = 15–30 cm): weather radar, long-range surveillance. S-band (2–4 GHz, λ = 7.5–15 cm): airport surveillance, some weather radar. X-band (8–12 GHz, λ = 2.5–3.75 cm): airborne weather radar, marine radar. W-band (75–110 GHz, λ = 2.7–4 mm): automotive radar (77 GHz), high-resolution imaging. Shorter wavelength → better resolution but more atmospheric absorption and shorter range. A target must be larger than λ/10 to reflect efficiently — X-band detects targets >3 mm; L-band misses small objects.