Wave Speed Calculator

Compute wave speed — wavelength, frequency, or speed — with the underlying wave equation.

Quick Facts

Wave equation
v = f × λ
Speed equals frequency times wavelength for any periodic wave.
Period
T = 1 / f
Period is the time for one full cycle; frequency is its reciprocal.
Light in vacuum
c ≈ 2.998 × 10⁸ m/s
All electromagnetic waves travel at this speed in a vacuum, regardless of frequency.
Sound in air
≈ 343 m/s (20°C)
Unlike light, sound speed depends heavily on the medium and temperature.

Your Results

Calculated
Wave Speed
-
v = f × λ
Frequency
-
f = v / λ
Wavelength
-
λ = v / f
Period
-
T = 1 / f

Ready

Choose what to solve for, enter the other two values, then press Calculate.

How the Wave Speed Calculator Works

Every periodic wave — sound, light, a ripple on water, a pulse on a guitar string — obeys the same relationship between how fast it travels, how often it oscillates, and how far apart its repeating crests are. That relationship is the wave equation: v = f × λ, where v is wave speed, f is frequency, and λ (lambda) is wavelength. Give this calculator any two of those three quantities and it solves for the third.

Deriving v = f × λ

In one full oscillation, a wave source completes one cycle in a time called the period, T. During that same time, the wave front advances exactly one wavelength, λ. Speed is distance divided by time, so v = λ / T. Since frequency is the reciprocal of period (f = 1/T), substituting gives v = λ × f, the wave equation. Rearranging it solves for whichever quantity is unknown: f = v / λ when you know speed and wavelength, or λ = v / f when you know speed and frequency.

Frequency stays fixed when a wave changes medium

Wave speed is a property of the medium the wave travels through — sound moves faster in water than in air, and light slows down when it enters glass. Frequency, by contrast, is set by the source and does not change as the wave crosses into a new medium. Because v = f × λ must still hold, wavelength is the quantity that adjusts: when speed drops, wavelength shrinks by the same factor. This is exactly what happens during refraction, and it is why the "solve for wavelength" and "solve for frequency" modes above are just as useful as solving for speed.

Typical wave speeds worth knowing

  • Light in a vacuum: c ≈ 2.998 × 10⁸ m/s — the universal speed limit, unaffected by frequency.
  • Sound in dry air at 20°C: ≈ 343 m/s; sound travels roughly 4.3 times faster in water (≈1,480 m/s) because liquids are stiffer than gases.
  • Waves on a stretched string: v = √(T/μ), where T is string tension and μ is mass per unit length — a separate formula used for musical strings, not the general v = f × λ relation.
  • Seismic P-waves through rock: roughly 5,000-8,000 m/s depending on rock density and rigidity.

Frequently Asked Questions

What is the wave speed formula?
Wave speed equals frequency multiplied by wavelength: v = f × λ. This applies to any periodic wave — sound, light, water waves, or a wave on a string — as long as f is in hertz and λ is in meters, giving v in meters per second.
How do I find frequency or wavelength instead of speed?
Rearrange the wave equation: frequency is f = v / λ, and wavelength is λ = v / f. Use whichever two quantities you already know to solve for the third.
Why does wavelength change when a wave enters a new medium, but frequency doesn't?
Frequency is set by the wave's source and stays constant as the wave crosses into a new medium. Speed changes because it depends on the medium's properties, so wavelength must adjust (λ = v/f) to keep the equation balanced — this is exactly what happens when light refracts entering glass or water.
How fast do sound and light waves actually travel?
Light in a vacuum travels at c ≈ 2.998 × 10⁸ m/s, the fastest speed information can travel. Sound in dry air at 20°C moves much slower, about 343 m/s, and at different speeds in other media — around 1,480 m/s in water and roughly 5,000-6,000 m/s in steel.

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