frequencytowavelength

Frequency to wavelength refers to the relationship between the frequency (f) of a wave and its wavelength (λ). For any wave, speed v is the product of frequency and wavelength: v = f λ. Consequently, wavelength is inversely proportional to frequency: λ = v / f.

In vacuum, for electromagnetic waves, the speed v is the constant c, about 299,792,458 meters per second, giving λ = c / f. Thus higher frequency light has shorter wavelength, and lower frequency light has longer wavelength. For example, a radio wave at 100 MHz has λ ≈ 3 meters; visible light around 5×10^14 Hz has λ in the 400–700 nm range.

In a material medium, wave speed is v = c / n for light, where n is refractive index. The wavelength becomes λ = v / f = c / (n f). When light crosses a boundary, its frequency remains unchanged, but its wavelength changes due to the change in speed.

For sound waves, speed in air is about 343 m/s; thus f λ = v, so λ = v / f. A 343 Hz tone has a wavelength of about 1 meter in air at room temperature.

In dispersive media, velocity depends on frequency, so the f-λ relation is not a simple inverse with a constant v; λ(f) = v(f) / f. In non-dispersive media, v is roughly constant over the frequencies of interest, making λ ∝ 1/f.

Applications include tuning radios, fiber optics, and microscopy; understanding the relation helps interpret spectra and design systems that rely on specific wavelengths or frequencies.