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.
Solve for
Wave Type
Media Presets (fills wave speed)
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
- 1Select what to solve for: Click one of the four mode tabs — Solve for v, Solve for f, Solve for λ, or Solve for T.
- 2Enter 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.
- 3Optionally 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.
- 4Select wave type (optional): Choose Mechanical or Electromagnetic. Selecting EM enables the spectrum classification label on the result.
- 5Press 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
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:
- ›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
Does the calculator save my inputs?
All inputs are persisted to your browser's localStorage:
- ›Solve mode (v / f / λ / T) is remembered
- ›All field values and their selected units are saved
- ›Wave type (Mechanical / Electromagnetic) is preserved
- ›Data stays in your browser — nothing is sent to any server
- ›Click Reset All to clear the form and delete saved data