Wavelength Calculator
Calculate wavelength, frequency, and wave speed for electromagnetic and mechanical waves
Wavelength (λ)
Frequency (f)
Wave Speed (v)
Period (T)
Photon Energy (E)
Electromagnetic Spectrum
About the Wave Equation
The wave equation describes the fundamental relationship between wavelength, frequency, and wave speed. It applies to all types of waves, including electromagnetic waves (light, radio, X-rays) and mechanical waves (sound, water waves, seismic waves).
Key Equations
- v = f × λ — Wave equation (speed = frequency × wavelength)
- λ = v / f — Wavelength from speed and frequency
- f = v / λ — Frequency from speed and wavelength
- T = 1 / f — Period (inverse of frequency)
- E = hf — Photon energy (Planck's equation, for electromagnetic waves)
Variables
- λ (lambda) — Wavelength (m)
- f — Frequency (Hz, cycles per second)
- v — Wave speed (m/s)
- T — Period (s)
- E — Photon energy (J or eV, electromagnetic waves only)
- h — Planck's constant (6.626 × 10⁻³⁴ J·s)
- c — Speed of light in vacuum (2.998 × 10⁸ m/s)
Electromagnetic Spectrum
Electromagnetic waves span a vast range of wavelengths and frequencies. All electromagnetic waves travel at the speed of light in vacuum (c ≈ 2.998 × 10⁸ m/s), but they differ in wavelength and frequency, which determine their properties and applications.
| Wave Type | Wavelength Range | Frequency Range | Common Uses |
|---|---|---|---|
| Radio Waves | > 1 mm | < 300 GHz | Broadcasting, communication, radar |
| Microwaves | 1 mm – 1 m | 300 MHz – 300 GHz | Cooking, Wi-Fi, satellite |
| Infrared | 700 nm – 1 mm | 300 GHz – 430 THz | Thermal imaging, remote controls |
| Visible Light | 380 nm – 700 nm | 430 THz – 790 THz | Human vision, photography, fiber optics |
| Ultraviolet | 10 nm – 380 nm | 790 THz – 30 PHz | Sterilization, fluorescence, tanning |
| X-rays | 0.01 nm – 10 nm | 30 PHz – 30 EHz | Medical imaging, security screening |
| Gamma Rays | < 0.01 nm | > 30 EHz | Cancer treatment, nuclear physics, astronomy |
Speed of Sound in Different Media
Unlike electromagnetic waves, mechanical waves such as sound require a medium to travel through. The speed of sound varies significantly depending on the medium's density and elasticity.
Air (at 20°C)
- • Speed: ~343 m/s
- • Increases with temperature
- • Human hearing: 20 Hz – 20 kHz
- • Wavelengths: ~17 mm – 17 m
Water (at 25°C)
- • Speed: ~1,480 m/s
- • ~4.3× faster than in air
- • Used in sonar and marine biology
- • Varies with salinity and depth
Steel
- • Speed: ~5,960 m/s
- • ~17× faster than in air
- • Used in ultrasonic testing
- • High elasticity enables fast propagation
References
The physical constants and wave data used in this calculator are based on established scientific standards:
Related Calculators
Note: This calculator uses standard physical constants (speed of light c = 299,792,458 m/s, Planck's constant h = 6.626 × 10⁻³⁴ J·s). Speed of sound values are approximations at standard conditions. Actual wave speeds vary with temperature, pressure, and medium properties.
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