What is the speed of light?

The speed of light in a vacuum is exactly c = 299,792,458 m/s (approximately 3 × 10⁸ m/s). All electromagnetic waves (radio, visible light, X-rays) travel at this speed in vacuum but slow slightly in other media.

How do I convert frequency to wavelength?

Use λ = v / f. For a radio wave at 100 MHz in vacuum: λ = 299,792,458 / 100,000,000 = 2.998 m ≈ 3 m. For sound at 1000 Hz in air (343 m/s): λ = 343 / 1000 = 0.343 m = 34.3 cm.

Wave Speed Calculator

Solve v = f × λ for wave speed, frequency, or wavelength. Supports sound, light, radio waves and more — with medium presets and derived quantities.

Solve for:

Presets:

Medium Preset

Wave Speed (v)

Frequency (f)

Wavelength (λ)

Fill in two known values — the third is calculated automatically.

What Is a Wave?

A wave is a disturbance that transfers energy through a medium (or through space, in the case of electromagnetic waves) without permanently displacing the medium itself. Waves are characterised by wavelength, frequency, amplitude, and speed.

Examples include sound waves (pressure disturbances in air), water waves (surface oscillations), electromagnetic waves (light, radio, X-rays), and seismic waves (vibrations in Earth's crust).

The Wave Equation v = fλ

Solve for Speed

v = f × λ

Given frequency and wavelength.

Solve for Frequency

f = v / λ

Given speed and wavelength.

Solve for Wavelength

λ = v / f

Given speed and frequency.

Period: T = 1/f

Angular Freq: ω = 2πf

Wavenumber: k = 2π/λ

Speed of Common Waves

Wave / Medium	Speed (m/s)	Notes
Sound in air (20°C)	343	Increases ~0.6 m/s per °C
Sound in air (0°C)	331	Reference at 0°C dry air
Sound in fresh water	1,480	At 20°C
Sound in seawater	1,520	Varies with salinity/depth
Sound in steel	5,960	Longitudinal wave
Ultrasound in tissue	1,540	Used in medical imaging
Light in vacuum (c)	299,792,458	Exact by definition
Light in glass	~200,000,000	Depends on refractive index
Ocean surface wave	5–30	Depends on depth/wavelength

EM Spectrum Reference

Type	Frequency range	Wavelength range
Radio	< 300 MHz	> 1 m
Microwave	300 MHz – 300 GHz	1 mm – 1 m
Infrared (IR)	300 GHz – 430 THz	700 nm – 1 mm
Visible light	430 – 770 THz	390 – 700 nm
Ultraviolet (UV)	770 THz – 30 PHz	10 – 400 nm
X-ray	30 PHz – 30 EHz	0.01 – 10 nm
Gamma ray	> 30 EHz	< 0.01 nm

Worked Examples

Example 1 — Middle C in air

v = 343 m/s, f = 261.6 Hz

λ = v / f = 343 / 261.6

λ = 1.311 m

Example 2 — Red light (700 nm)

v = 299,792,458 m/s, λ = 700 nm

f = v / λ = 2.998×10⁸ / 7×10⁻⁷

f ≈ 428.3 THz

Example 3 — FM Radio 100 MHz

v = c, f = 100 MHz = 10⁸ Hz

λ = 2.998×10⁸ / 10⁸

λ ≈ 3.0 m

Example 4 — Find wave speed

f = 200 Hz, λ = 1.715 m

v = f × λ = 200 × 1.715

v = 343 m/s (sound in air)

Frequently Asked Questions

Wave speed is the rate at which a wave disturbance travels through a medium. It is measured in metres per second (m/s) and determined by the equation v = f × λ, where f is frequency and λ is wavelength.

No — for most waves in a given medium, wave speed is a property of the medium, not the frequency. Changing frequency changes wavelength proportionally so the product v = fλ stays constant. For light in a dispersive medium, speed can vary slightly with frequency (dispersion).

The speed of sound in dry air at 20°C is approximately 343 m/s (about 1235 km/h or 767 mph). It increases with temperature: roughly 0.6 m/s for each 1°C rise. In air at 0°C it is about 331 m/s.

The speed of light in a vacuum is exactly c = 299,792,458 m/s (approximately 3 × 10⁸ m/s). All electromagnetic waves travel at this speed in vacuum but slow slightly in other media.

Use λ = v / f. For a radio wave at 100 MHz in vacuum: λ = 299,792,458 / 100,000,000 ≈ 3.0 m. For sound at 1000 Hz in air (343 m/s): λ = 343 / 1000 = 0.343 m = 34.3 cm.

Transverse waves oscillate perpendicular to their direction of travel (e.g. light, water surface waves). Longitudinal waves oscillate parallel to their travel direction via compressions and rarefactions (e.g. sound, seismic P-waves). Both obey v = fλ.

Sound speed depends on the medium's bulk modulus (stiffness) and density: v = √(B/ρ). Water is much stiffer (higher bulk modulus) than air, which more than compensates for its higher density. Sound travels at ~1480 m/s in water vs ~343 m/s in air.

Period T (seconds) and frequency f (Hz) are reciprocals: T = 1/f and f = 1/T. A 100 Hz wave completes 100 cycles per second, so its period is 0.01 s = 10 ms. A 0.1 Hz ocean wave has a period of 10 seconds.

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