Wave Equation Calculator (Travelling Wave)
Travelling wave y = A·sin(kx − ωt + φ): enter any two of frequency, wavelength and speed to get ω, k, period and the displacement and velocity at a point.
How to use the Wave Equation Calculator
- Enter or select: Amplitude A, Position x, Time t, Phase φ.
- Fill in what you know of: Frequency f, Wavelength λ, Wave speed v — leave the unknown empty.
- The results (Frequency, Wavelength, Wave speed, Period, Angular frequency ω, Wave number k, Displacement y(x,t), Transverse velocity ∂y/∂t) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- ∂²y/∂t² = v² ∂²y/∂x²
- y(x,t) = A sin(kx − ωt + φ)
- v = fλ = ω/k
About this tool
The one-dimensional wave equation is satisfied by any function of (x − vt) or (x + vt); the sinusoid is the single-frequency solution.