Wave Properties Calculator
Compute the wavelength of any wave from its speed and frequency using λ = v/f. Works for sound, light, water waves, and any other wave phenomenon — useful in acoustics, optics, radio engineering, and physics homework.
Last updated: May 2026
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About this calculator
The fundamental wave equation links three quantities: v = f·λ, where v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m). Rearranging gives λ = v/f (wavelength from speed and frequency) and f = v/λ (frequency from speed and wavelength). The period T — how long one full oscillation takes — is the reciprocal of frequency: T = 1/f. Wave speed depends on the medium: light in vacuum travels at exactly c = 299,792,458 m/s; light in glass at about 2 × 10⁸ m/s (refractive index ~1.5); sound in air at about 343 m/s at 20 °C (scaling with temperature as v ≈ 331 + 0.6·T m/s); sound in water at about 1,500 m/s. The medium selector pre-loads common values. Edge cases: at extremely high frequencies (gamma rays, ~10²⁰ Hz) wavelengths shrink to subatomic scales (~10⁻¹² m), where matter behaves differently and quantum effects dominate. Conversely, ultra-low-frequency waves (sub-Hz, like Earth’s Schumann resonances near 7.83 Hz) have wavelengths of tens of thousands of kilometres. The amplitude field is informational only — amplitude doesn’t enter into v = f·λ; it describes the wave’s height but not how fast it travels. Sound is longitudinal and EM is transverse, but the wavelength-frequency relation is identical for both. The formula applies to monochromatic (single-frequency) waves; complex waveforms like speech or music are decomposed into many such single-frequency components via Fourier analysis.
How to use
Example 1 — Wavelength of a concert-A note. You want the wavelength of A4 (440 Hz) in air at 20 °C, where sound travels at 343 m/s. λ = v/f = 343/440 ≈ 0.780 m ≈ 78 cm. ✓ Period T = 1/440 ≈ 2.27 ms — the air-pressure oscillation rate at your ear. Example 2 — Wavelength of green laser light. A green laser at 532 nm: set wave speed = 299,792,458 (light in vacuum) and frequency = 5.64e14. λ = 299,792,458 / 5.64×10¹⁴ ≈ 5.32 × 10⁻⁷ m = 532 nm. ✓ In glass (n ≈ 1.5) the speed drops to 2 × 10⁸ m/s and the wavelength compresses to ~355 nm while frequency stays at 5.64 × 10¹⁴ Hz — frequency is set by the source; wavelength shifts with the medium.
Frequently asked questions
Why does frequency stay constant when a wave enters a new medium, but wavelength changes?
Frequency is set by the source — a tuning fork vibrating at 440 Hz produces a sound wave whose pressure oscillates 440 times per second, and that oscillation rate is a property of the wave itself, not the medium. When the wave enters a new medium (air → water, vacuum → glass), the speed v changes because the medium’s elastic and inertial properties differ, but the frequency remains the same because the source still oscillates at the same rate. The wavelength has to compensate to satisfy v = f·λ: if v drops by half and f stays constant, λ drops by half too. This is why a violin sounds the same pitch underwater (frequency unchanged) but with a different timbre. It is also why refraction works — light slowing down in glass shortens its wavelength while keeping frequency constant, and the change in wavelength produces the bending.
What is the difference between frequency and period?
Frequency (f) counts oscillations per second, measured in hertz; period (T) measures the duration of one full oscillation, in seconds. They are exact reciprocals: T = 1/f and f = 1/T. A 50 Hz mains AC waveform has a period of 20 ms (one full sine-wave cycle every 0.02 seconds). A 60 Hz signal has period 16.67 ms. A 1 GHz CPU clock has period 1 ns — one full clock cycle in a billionth of a second. Frequency is more intuitive for talking about pitch, colour, and repetition rate; period is more useful for thinking about timing, pulse widths, and signal latency. Both contain the same information; engineers switch between them depending on what is natural for the problem.
Why is the speed of light treated as a universal constant?
In any inertial reference frame and in vacuum, light always travels at exactly c = 299,792,458 m/s — one of the two postulates of Einstein’s special relativity (1905), and decades of experiments have failed to find any deviation. The constancy of c led directly to the conclusion that space and time must be relative (length contraction, time dilation) because for everyone to measure the same c regardless of their motion, their rulers and clocks must distort. In media (glass, water, air), light slows because it scatters off electrons and gets re-emitted with a slight delay — the apparent group velocity in glass is c/n, where n is the refractive index (typically 1–2 for common materials). The fundamental constant is the vacuum speed, not the in-medium speed. Since 1983 the metre has been defined in terms of c, making the value 299,792,458 m/s exact by definition rather than measurement.
What are the most common mistakes people make with the wave equation?
The first is using the wrong wave speed for the medium — assuming v = 343 m/s when the wave is in water (should be 1,500 m/s) gives a wavelength that is a factor of 4 off. The second is mixing units of frequency: hertz (Hz), kilohertz (kHz = 10³), megahertz (MHz = 10⁶), and gigahertz (GHz = 10⁹) all describe the same thing, but mixing prefixes causes order-of-magnitude errors. The third is forgetting that wavelength and frequency are inversely related; doubling frequency halves wavelength, not doubles it. The fourth is treating v = f·λ as if it applied to amplitude — amplitude is separate, controlled by source intensity, and doesn’t enter the relation. The fifth is using non-vacuum speeds where they shouldn’t apply (e.g., quoting wavelength of 532 nm light ‘in glass’ as 532 nm — it is actually ~355 nm in glass because v changes). Finally, in dispersive media there is a distinction between phase velocity and group velocity that v = f·λ obscures.
When should I not use this calculator?
Skip it for non-sinusoidal or impulsive signals — a single pulse or chirp doesn’t have one wavelength but a whole spectrum of them, requiring Fourier analysis. Avoid it for matter waves (electrons, neutrons, atoms in interference experiments) — those use the de Broglie relation λ = h/p (Planck’s constant divided by momentum), not v/f, and operate at quantum scales. It is not the right tool for shallow-water or surface-gravity waves where the dispersion relation is more complex than v = f·λ. Do not use it for non-linear waves like shock waves in air or solitons in optical fibres, where the simple linear wave equation doesn’t apply. And for problems involving the Doppler effect (frequency shift due to relative motion between source and observer), you need Doppler corrections before using v = f·λ. For ordinary linear, sinusoidal waves in a single medium — sound in air, light in vacuum, radio in free space, EM radiation in any uniform material — this is the right and complete tool.