How to Calculate Wavelength and Frequency
All waves—light, sound, radio, seismic—share a fundamental relationship between wavelength, frequency, and wave speed. Understanding this relationship is essential in physics, telecommunications, and acoustics.
The Wave Speed Equation
v = f × λ
Where:
- v = wave speed (m/s)
- f = frequency (Hz = cycles per second)
- λ (lambda) = wavelength (m)
Rearrangements:
- f = v / λ
- λ = v / f
Light Waves
The speed of light in a vacuum is c = 3 × 10⁸ m/s.
Example: Find the wavelength of blue light with frequency 6.5 × 10¹⁴ Hz. λ = c / f = (3 × 10⁸) / (6.5 × 10¹⁴) = 4.62 × 10⁻⁷ m = 462 nm (blue-violet)
Sound Waves
The speed of sound in air at 20°C is approximately 343 m/s.
Example: Find the wavelength of middle C (262 Hz) in air. λ = 343 / 262 = 1.31 meters
Example: Find the frequency of a sound wave with wavelength 0.5 m. f = 343 / 0.5 = 686 Hz (within the hearing range of 20 Hz–20,000 Hz)
Electromagnetic Spectrum
| Radiation | Frequency (Hz) | Wavelength |
|---|---|---|
| Radio | 10³–10⁹ | 0.3 mm – 300 km |
| Microwave | 10⁹–10¹² | 0.3 mm – 30 cm |
| Infrared | 10¹²–4×10¹⁴ | 700 nm – 300 μm |
| Visible light | 4–7.5×10¹⁴ | 400–700 nm |
| Ultraviolet | 7.5×10¹⁴–10¹⁷ | 10–400 nm |
| X-rays | 10¹⁷–10²⁰ | 0.01–10 nm |
Use our wavelength and frequency calculator for any wave type.