Physics

Wave Speed Calculator | v = fλ

Calculate wave speed, frequency, wavelength, or period using v = fλ. Supports sound, light, and all wave types across different media with unit conversion.

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Solve for

Wave Type

Media Presets (fills wave speed)

Wave Speed (v)

Frequency (f)

Enter calculate · Esc reset

What Is the Wave Speed Calculator | v = fλ?

This wave speed calculator solves for any one of the four wave quantities: speed (v), frequency (f), wavelength (λ), or period (T), when the other two are known. It supports everything from sound waves in air and water to visible light and radio waves.

›Solve for any variable, choose which quantity to find; the calculator automatically shows the two required input fields and hides the rest.
›Multi-unit support, enter speed in m/s, km/s, km/h, mph, or ft/s; frequency in Hz, kHz, MHz, GHz, or THz; wavelength in nm, μm, mm, cm, m, or km; and period in ns, μs, ms, or s. All conversions are handled internally.
›Media presets, one-click presets for sound in air (343 m/s), sound in water (1,480 m/s), sound in steel (5,960 m/s), light in vacuum (299,792,458 m/s), and light in glass (~200,000,000 m/s).
›EM spectrum classification, when solving for a frequency in the electromagnetic spectrum, the calculator labels the result as Radio, Microwave, Infrared, Visible, UV, X-ray, or Gamma ray.

Formula

Core Wave Equations

v = f × λ (speed = frequency × wavelength)

f = v / λ (frequency = speed ÷ wavelength)

λ = v / f (wavelength = speed ÷ frequency)

Period & Frequency

T = 1 / f (period = reciprocal of frequency)

v = λ / T (speed = wavelength ÷ period)

Symbol	Name	Description
v	Wave Speed	Speed at which the wave propagates through a medium (m/s)
f	Frequency	Number of wave cycles per second (Hz = cycles/s)
λ	Wavelength	Distance between successive wave crests or troughs (m)
T	Period	Time for one complete wave cycle; T = 1/f (s)

How to Use

1
Select what to solve for: Click one of the four mode tabs, Solve for v, Solve for f, Solve for λ, or Solve for T.
2
Enter the known values: Two input fields appear. Type the two values you know. Use the unit dropdown next to each field to match the units you have.
3
Optionally use a media preset: Click "Sound in Air", "Sound in Water", "Light in Vacuum", etc. to auto-fill the wave speed field with a known value.
4
Select wave type (optional): Choose Mechanical or Electromagnetic. Selecting EM enables the spectrum classification label on the result.
5
Press Enter or click Calculate: The result appears in a highlighted card showing the solved value, plus all four derived quantities (v, f, λ, T) in a summary grid.

Example Calculation

Example 1: Sound, Musical A note (440 Hz) in air

Given: v = 343 m/s (speed of sound in air), f = 440 Hz

Solve for λ: λ = v / f

λ = 343 / 440

λ ≈ 0.7795 m ≈ 77.95 cm

Period: T = 1 / f = 1 / 440

T ≈ 0.002273 s ≈ 2.27 ms

Example 2: Light, Green light (550 nm) in vacuum

Given: v = 299,792,458 m/s (speed of light), λ = 550 nm = 5.50 × 10⁻⁷ m

Solve for f: f = v / λ

f = 299,792,458 / (5.50 × 10⁻⁷)

f ≈ 5.45 × 10¹⁴ Hz = 545 THz

EM Classification: Visible Light (green)

Quick reference: wave speed in common media

Sound in air (20°C): 343 m/sSound in water (25°C): 1,480 m/sSound in steel: 5,960 m/sLight in vacuum: 299,792,458 m/sLight in glass (n≈1.5): ~200,000,000 m/sLight in water (n≈1.33): ~225,000,000 m/s

Understanding Wave Speed | v = fλ

The Wave Speed Equation

The fundamental relationship v = fλ holds for all periodic waves, sound, light, water, seismic, radio, and more. It says that a wave travelling at speed v completes f cycles per second, and each cycle spans a distance of λ metres. Double the frequency and the wavelength halves; triple the speed and the wavelength triples (if f stays constant).

The period T = 1/f is the time for one complete cycle. Substituting gives the equivalent form v = λ/T, which is useful when period rather than frequency is measured directly (e.g., ocean wave heights measured every few seconds).

Speed of Sound in Different Media

Sound is a mechanical wave, it requires a medium to travel through. Its speed depends on two properties of the medium: elasticity (restoring force) and density. Stiffer, less dense materials transmit sound faster.

Medium	Speed (m/s)	Notes
Air (20°C)	343	Increases ~0.6 m/s per °C rise
Air (0°C)	331	Reference temperature
Water (25°C)	1,480	~4.3× faster than air
Seawater	1,520	Salinity raises speed slightly
Steel	5,960	Very high elasticity, low density
Aluminium	6,320	Common in engineering
Diamond	12,000	Highest known solid value
Helium gas	965	Low density, high elasticity

Speed of Light and the EM Spectrum

Electromagnetic waves, radio, microwave, infrared, visible light, UV, X-ray, and gamma ray, all travel at c = 299,792,458 m/s in vacuum. In a medium with refractive index n, the speed drops to c/n (e.g., glass n ≈ 1.5 gives v ≈ 200,000,000 m/s). The frequency does not change when light enters a medium; only the wavelength shrinks.

›Radio waves: f < 300 GHz, λ > 1 mm, used in communication, broadcasting
›Microwave: 300 MHz–300 GHz, λ = 1 mm–1 m, radar, Wi-Fi, microwave ovens
›Infrared: 300 GHz–400 THz, λ = 700 nm–1 mm, thermal imaging, remote controls
›Visible light: 400–700 THz, λ = 400–700 nm, the only range the human eye detects
›Ultraviolet: 700 THz–30 PHz, λ = 10–400 nm, causes sunburn, used in sterilisation
›X-ray: 30 PHz–30 EHz, λ = 0.01–10 nm, medical imaging, crystallography
›Gamma ray: f > 30 EHz, λ < 0.01 nm, nuclear decay, highest energy photons

Period vs Frequency

Period (T) and frequency (f) are reciprocals: T = 1/f. A wave with f = 1,000 Hz completes 1,000 cycles per second, so each cycle takes T = 0.001 s = 1 ms. Engineers in electronics often work in frequency (Hz, kHz, MHz), while oceanographers and seismologists often measure period directly (seconds, minutes). The calculator handles both, and converts automatically.

Real-World Applications

Application	Wave Type	Typical f or λ
Human hearing range	Sound	20 Hz – 20,000 Hz
Ultrasound (medical)	Sound	1 MHz – 20 MHz
FM radio	EM (radio)	87.5 – 108 MHz
Wi-Fi 2.4 GHz	EM (microwave)	2.4 GHz, λ ≈ 12.5 cm
Visible light (green)	EM (visible)	550 nm, 545 THz
Chest X-ray	EM (X-ray)	0.01–0.1 nm
Ocean swell	Water surface	T = 10–20 s, λ = 150–600 m
Earthquake P-wave	Seismic	1–10 Hz, v ≈ 6 km/s in crust

Frequently Asked Questions

What determines the speed of a wave?

Wave speed is a property of the medium, not of the wave's frequency or wavelength:

›Sound: v = √(Elasticity / Density), stiffer, lighter materials = faster speed
›EM waves in vacuum: always c = 299,792,458 m/s regardless of frequency
›EM waves in a medium: v = c / n, where n is the refractive index (n ≥ 1)
›Changing f in the same medium shifts λ, keeping v constant

Temperature affects sound speed: in air, v ≈ 331 + 0.6 × T°C (m/s).

Why is sound slower than light?

Sound and light are fundamentally different types of waves:

›Sound: mechanical, needs a medium; speed limited by intermolecular collisions
›Light: electromagnetic; can travel through vacuum; limited only by c
›Speed ratio: c / v_sound ≈ 299,792,458 / 343 ≈ 874,000 in air
›Consequence: you see lightning before you hear thunder (~3 seconds per km)

If I double the frequency, what happens to the wavelength?

In the same medium (constant v), frequency and wavelength are inversely proportional:

v = f × λ → λ = v / f

›Double f → halve λ (same wave speed)
›Triple f → reduce λ to one-third
›Halve f → double λ (same wave speed)

Musical octaves work this way: each octave doubles frequency, halving wavelength. The A4 note (440 Hz) and A5 (880 Hz) have wavelengths of 0.780 m and 0.390 m respectively in air at 20°C.

Why does sound travel faster in water than in air?

Speed of sound = √(Bulk modulus / Density):

›Air: K ≈ 142 kPa, ρ ≈ 1.2 kg/m³ → v ≈ 343 m/s
›Water: K ≈ 2.2 GPa, ρ ≈ 1,000 kg/m³ → v ≈ 1,480 m/s
›Steel: K ≈ 160 GPa, ρ ≈ 7,800 kg/m³ → v ≈ 5,960 m/s
›Elasticity outweighs density: despite water being 830× denser than air, its elasticity is 15,000× higher

What is the electromagnetic spectrum?

All EM waves travel at c in vacuum but differ in frequency and wavelength:

›Radio: f < 300 MHz, λ > 1 m, AM/FM, TV, mobile networks
›Microwave: 300 MHz–300 GHz, λ = 1 mm–1 m, radar, Wi-Fi, satellite
›Infrared: 300 GHz–400 THz, λ = 700 nm–1 mm, heat, night vision
›Visible: 400–700 THz, λ = 400–700 nm, violet to red
›UV: 700 THz–30 PHz, λ = 10–400 nm, sunburn, sterilisation
›X-ray: 30 PHz–30 EHz, λ = 0.01–10 nm, medical imaging
›Gamma: > 30 EHz, λ < 0.01 nm, nuclear reactions, highest energy

How do I use the wave speed calculator for light?

Quick steps for light calculations:

›Click the "Light in Vacuum" preset → fills v = 299,792,458 m/s
›Set wave type to "Electromagnetic" to enable spectrum classification
›Select "Solve for f" and enter λ in nm (e.g., 550 nm)
›Click Calculate, result shows f ≈ 545 THz labelled as "Visible Light"
›For radio waves, enter f in MHz; wavelength appears in metres

Tip

Wavelengths for visible light run from violet (~400 nm) to red (~700 nm). X-ray wavelengths are measured in pm (picometres), use the nm unit and enter e.g. 0.1 nm.