What is the relationship between wavelength and frequency?

Wavelength and frequency are inversely proportional for any wave travelling at a fixed speed: v = fλ, so f = v/λ and λ = v/f. For light in a vacuum, v = c = 2.998 × 10⁸ m/s. A longer wavelength means a lower frequency, and vice versa.

What is the frequency of visible light?

Visible light spans roughly 380–700 nm in wavelength, corresponding to frequencies of approximately 4.3 × 10¹⁴ Hz (red, 700 nm) to 7.9 × 10¹⁴ Hz (violet, 380 nm). These are often expressed in THz (terahertz): about 430–790 THz.

How do wavelength and frequency relate for sound?

Sound travels at approximately 343 m/s in air at 20°C. A 440 Hz note (concert A) has a wavelength of 343/440 ≈ 0.78 m. For sound, the wave speed changes with medium — 1,480 m/s in water and ~5,100 m/s in steel.

Science

Wavelength–Frequency Calculator

Calculate wavelength, frequency, or wave speed from any two known values using the wave equation v = fλ. Works for light, sound, radio waves, and all other wave types.

Fill in any two values — the third will be calculated automatically.

Wave type (sets default speed)

Wavelength (m)

Frequency (Hz)

Wave speed (m/s)

Result

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Wavelength—

Frequency—

Wave speed—

Formula used—

The wave equation

v = f × λ v = wave speed (m/s) f = frequency (Hz) λ = wavelength (m) Rearranged: f = v / λ λ = v / f

Worked examples

Example 1 — What is the wavelength of a 100 MHz FM radio signal?

f = 100 MHz = 1.0 × 10⁸ Hz, v = c = 2.998 × 10⁸ m/s λ = v/f = 2.998×10⁸ / 1.0×10⁸ = 3.0 m FM antennas are typically λ/4 = 0.75 m long (quarter-wave)

Example 2 — What frequency is 440 nm blue light?

λ = 440 nm = 4.4 × 10⁻⁷ m, v = c = 2.998 × 10⁸ m/s f = v/λ = 2.998×10⁸ / 4.4×10⁻⁷ = 6.81 × 10¹⁴ Hz = 681 THz This is in the violet-blue region of visible light

Example 3 — Wavelength of middle C (261.6 Hz) in air:

f = 261.6 Hz, v = 343 m/s (air at 20°C) λ = v/f = 343 / 261.6 = 1.31 m Sound wavelengths are much longer than light wavelengths

Applications of the wave equation

Antenna design: Radio antennas are designed to be a specific fraction of the signal wavelength (typically λ/4 or λ/2). A 2.4 GHz WiFi signal has λ = 12.5 cm, so a quarter-wave antenna is about 3.1 cm — matching the size of internal antennas in smartphones.

Musical acoustics: The resonant frequencies of wind instruments depend on the wavelength fitting inside the tube. A closed-end tube of length L resonates at λ = 4L (fundamental). The wave equation v = fλ relates the physical length of the instrument to the notes it can produce.

Medical ultrasound: Ultrasound imaging uses frequencies of 2–18 MHz. At 5 MHz in tissue (v ≈ 1540 m/s), λ = 1540/5×10⁶ = 0.31 mm. This sets the resolution limit — features smaller than about λ/2 = 0.15 mm cannot be resolved.

Optical fibre communications: Telecom fibres operate at 1310 nm and 1550 nm wavelengths where silica glass has minimum absorption and dispersion. The 1550 nm "C-band" supports dozens of simultaneous channels via wavelength division multiplexing (WDM), each at a slightly different wavelength.

Wave speed in different media

Wave type	Medium	Speed (m/s)
Light (EM)	Vacuum	2.998 × 10⁸
Light (EM)	Water (n=1.33)	2.25 × 10⁸
Light (EM)	Glass (n=1.5)	2.0 × 10⁸
Sound	Air (20°C)	343
Sound	Water	1,480
Sound	Steel	5,100
Sound	Concrete	3,200
Seismic (P-wave)	Rock (crust)	6,000–7,000

Common questions

Wavelength and frequency are inversely proportional for any wave travelling at a fixed speed: v = fλ, so f = v/λ and λ = v/f. For light in a vacuum, v = c = 2.998 × 10⁸ m/s. A longer wavelength means a lower frequency, and vice versa.
Visible light spans roughly 380–700 nm in wavelength, corresponding to frequencies of approximately 4.3 × 10¹⁴ Hz (red, 700 nm) to 7.9 × 10¹⁴ Hz (violet, 380 nm). These are often expressed in THz (terahertz): about 430–790 THz.
Sound travels at approximately 343 m/s in air at 20°C. A 440 Hz note (concert A) has a wavelength of 343/440 ≈ 0.78 m. For sound, the wave speed changes with medium — 1,480 m/s in water and ~5,100 m/s in steel.
For electromagnetic waves, v = c = 2.998 × 10⁸ m/s. λ = c/f = 2.998 × 10⁸ / (100 × 10⁶) = 3.0 m. FM radio signals have wavelengths in the 3 m range, which is why FM antennas are a fraction of a metre long.