Wave Equation Solver to Analyze Transverse and L...

The Wave Equation

The wave equation describes how waves propagate through space and time. Solving it tells you how a disturbance (sound, light, water, seismic) travels. The fundamental relationships between wave speed, frequency, and wavelength apply to all wave types.

〰️ Wave Equation Solver

Use our free calculator for instant, accurate results.

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📐 Formula

v = f × λ

v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m). Period T = 1/f. Wave equation: ∂²y/∂t² = v² × ∂²y/∂x².

📝 Worked Example

Green light: λ = 550 nm = 550×10⁻⁹ m, v = c = 3×10⁸ m/s:
f = v/λ = 3×10⁸/550×10⁻⁹ = 5.45×10¹⁴ Hz
T = 1/f = 1.83×10⁻¹⁵ s (1.83 femtoseconds per cycle)

📝 How to Use the Calculator

Enter Two PropertiesAny two of: wave speed, frequency, wavelength, period.

Select Wave TypeSound, light, water waves, or custom.

CalculateInstantly find all remaining wave properties.

View WaveformSee the sinusoidal wave y = A×sin(kx − ωt) with your parameters.

❓ FAQ

What is angular frequency?

ω = 2πf (radians/second). Angular wavenumber k = 2π/λ. These appear in the full wave equation y = A×sin(kx−ωt).

What is the difference between transverse and longitudinal waves?

Transverse: displacement perpendicular to propagation (light, water surface). Longitudinal: displacement parallel to propagation (sound, compression waves).

The Wave Equation