Wave calculator
Solve the universal wave equation for any variable, then keep going with period, string wave speed, energy and photon energy. Every result updates as you type and shows the substitution it used.
It works for any wave, because v = fλ does: a longitudinal sound wave, a ripple, or a photon anywhere on the electromagnetic spectrum.
Universal wave equation
v = f × λ
v = 200 × 0.5 = 100 m/s
Four more wave calculators
Period & frequency
T = 1 / f
Wave speed on a string
v = √(T / μ)
Energy from amplitude
E ∝ A²
Light: frequency & photon energy
c = fλ · E = hf
Every formula these calculators use
| Formula | What it gives you | Unit |
|---|---|---|
| v = f × λ | Universal wave equation — speed from frequency and wavelength | m/s |
| f = v / λ | Frequency from speed and wavelength | Hz |
| λ = v / f | Wavelength from speed and frequency | m |
| T = 1 / f | Period is the reciprocal of frequency | s |
| v = √(T / μ) | Wave speed on a stretched string | m/s |
| E ∝ A² | Wave energy scales with the square of amplitude | — |
| c = f × λ | Same equation for light, with v fixed at c | m/s |
| E = h × f | Photon energy from frequency (h = 6.626 × 10⁻³⁴ J·s) | J |
See the substitutions
A transverse wave has a frequency of 200 Hz and a wavelength of 0.5 m. What is its speed?
v = f × λ = 200 × 0.5 = 100 m/s
A guitar string is under 80 N of tension with a linear mass density of 0.005 kg/m. How fast do waves travel along it?
v = √(T / μ) = √(80 / 0.005) = √16,000 ≈ 126.5 m/s
Green light has a wavelength of 526 nm. What is its frequency?
f = c / λ = (3 × 10⁸) / (526 × 10⁻⁹) ≈ 5.7 × 10¹⁴ Hz
Calculator questions
How do you calculate wave speed?
Multiply frequency by wavelength: v = f × λ. If a wave has a frequency of 200 Hz and a wavelength of 0.5 m, its speed is 200 × 0.5 = 100 metres per second.
How do you find frequency from wavelength?
Divide the wave speed by the wavelength: f = v / λ. For light, use the speed of light (about 3 × 10⁸ m/s) as v.
What is the formula for wave speed on a string?
v = √(T / μ), where T is the tension in newtons and μ is the linear mass density in kg/m. Tightening the string raises the speed; a heavier string lowers it.
Does amplitude affect wave speed?
No. Amplitude sets how much energy the wave carries — energy is proportional to amplitude squared — but the speed depends only on the medium and on v = fλ.