Harmonic Wave Equation Calculator
Enter a wave’s amplitude, wavelength, and frequency, plus a position and time, to calculate its instantaneous displacement using the harmonic wave equation.
What is the harmonic wave equation?
A harmonic (sinusoidal) wave describes disturbances like sound, light, or waves on a string that repeat smoothly in both space and time. Its displacement at any point and moment follows a sine function.
The formula
The equation used here is y(x,t) = A × sin(kx − ωt), where A is amplitude, k = 2π/λ is the wave number, ω = 2πf is the angular frequency, x is position, and t is time. Wave speed is found separately from v = f × λ.
This models an idealized, non-attenuating traveling wave moving in the positive x-direction with no phase offset; real waves often include damping, superposition with other waves, or an initial phase constant. This calculator is for general physics education.