Wave speed, frequency, and wavelength are the three quantities that describe any travelling wave — from sound to light to water ripples. This calculator applies the fundamental wave equation v = f × λ to solve for whichever quantity you do not know. It also displays the period, angular frequency, and wave number in a secondary panel so that one calculation gives you everything you need for a textbook problem, engineering estimate, or quick unit conversion.
How it works
Every wave satisfies the wave equation:
v = f × λ
where v is the wave speed in metres per second, f is the frequency in hertz (cycles per second), and λ is the wavelength in metres. Rearranging:
- Frequency: f = v ÷ λ
- Wavelength: λ = v ÷ f
- Period: T = λ ÷ v (equivalent to T = 1 ÷ f)
The secondary quantities follow directly once f is known:
- Period: T = 1 ÷ f
- Angular frequency: ω = 2πf (rad/s)
- Wave number: k = 2π ÷ λ (rad/m)
The tool ships with four medium presets so you do not have to remember common speeds:
| Medium | Wave speed |
|---|---|
| Sound in air (~20 °C) | 343 m/s |
| Sound in water (~20 °C) | 1481 m/s |
| Sound in steel | 5120 m/s |
| Light in vacuum (c) | 299,792,458 m/s |
For any other situation — sound at altitude, ultrasound in tissue, microwaves in a waveguide — enter a custom speed.
Worked examples
Example 1 — Concert A (440 Hz, sound in air)
A 440 Hz tone travels through air at 343 m/s. Solving for wavelength:
λ = 343 ÷ 440 ≈ 0.780 m
The period is T = 1 ÷ 440 ≈ 2.27 ms, and the angular frequency is ω = 2π × 440 ≈ 2764 rad/s.
Example 2 — FM radio signal (100 MHz, light in vacuum)
An FM station at 100 MHz (100 × 10⁶ Hz) travels at the speed of light:
λ = 299,792,458 ÷ 100,000,000 ≈ 3.00 m
This is why FM antennas are roughly one to three metres long — they are sized at a fraction of the wavelength.
Example 3 — Sonar pulse in water
A sonar ping returns after 0.2 s. At 1481 m/s the round-trip distance is 1481 × 0.2 = 296 m, so the target is about 148 m away. For the sonar frequency of 20 kHz: λ = 1481 ÷ 20,000 ≈ 0.074 m (7.4 cm).
Why wave speed matters
Wave speed governs how fast energy and information travel. In acoustics, knowing wave speed lets engineers place microphones correctly, design concert halls, and specify ultrasound transducers. In electronics, it determines antenna dimensions and transmission-line delay. In optics, the ratio of the speed of light in a vacuum to its speed in a material defines the refractive index, which controls lenses and fibre-optic cables. For seismology, the wave speed of P-waves and S-waves through rock reveals the Earth’s interior structure. In every case, v = f × λ is the starting point.
All calculations run entirely in your browser — no values are sent to any server.