Harmonic Wave Equation Calculator

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Maximum displacement from equilibrium. Must be positive. Common units are metres (sound), pascals (pressure waves), or arbitrary units for normalised waves.
m
Distance over which the waveform repeats once (one full cycle). Together with frequency this fixes wave speed.
m
Number of complete oscillations per second. Period T = 1/f.
Hz
Initial phase offset in degrees. Use 0 for a pure sine, 90 for a cosine-like start. Positive phase shifts the wave to the left.
deg
Distance from the wave source along the direction of propagation at which displacement is evaluated.
m
Instant in time at which the displacement is evaluated. Must be zero or positive.
s
Displacement y(x, t)
2m

Instantaneous displacement of the medium at position x and time t

Wave speed (v)8m/s
Angular frequency (omega)12.5664rad/s
Wavenumber (k)1.5708rad/m
Period (T)0.5s
Phase argument-4.7124rad
Displacement (m)2
Wave speed (m/s)8
Period (s)0.5

Displacement is 2.0000 m at x = 1 m, t = 0.5 s.

  • The medium is at or very near its maximum amplitude (crest or trough).
  • Wave speed is 8.000 m/s: the disturbance travels 8.0 metres every second, completing 2.00 wavelengths per second.
  • One full oscillation takes 0.5000 s. Over 1 second there are 2 complete cycles.
  • The phase argument is near pi/2: the wave is at its positive peak.

Next stepVary the position x or time t to trace the wave in space or time. Use the waveform chart to see the full displacement profile at the chosen instant.

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