🌊 Wave & Simple Harmonic Motion Calculator
Enter amplitude, wavelength and frequency to see the wave drawn and get v, T, ω and k — or switch to simple harmonic motion for pendulum and spring periods.
Wave speed v = fλ
10 m/s
Period T = 1/f
0.2 s
Angular freq ω
31.416 rad/s
Wavenumber k
3.1416 rad/m
y = A·sin(kx − ωt). v = fλ · T = 1/f · ω = 2πf · k = 2π/λ.
🔒 Computed in your browser.
How the wave & simple harmonic motion calculator works
From amplitude A, wavelength λ and frequency f, the tool draws the sine wave y = A·sin(kx − ωt) and computes wave speed v = fλ, period T = 1/f, angular frequency ω = 2πf and wavenumber k = 2π/λ. The simple-harmonic-motion mode gives the pendulum period T = 2π√(L/g) and the mass-spring period T = 2π√(m/k).
One place for the wave relationships and the two classic SHM oscillators, with the wave shape drawn so amplitude and wavelength are visible.
Frequently asked questions
How do I calculate wave speed, period and wavenumber?
From frequency and wavelength: v = fλ, T = 1/f, ω = 2πf and k = 2π/λ. Enter amplitude, wavelength and frequency and the tool reports all four and plots the wave.
What is the period of a pendulum?
T = 2π√(L/g), where L is the length and g gravity — for small swings (under ~15°). A 1 m pendulum on Earth has a period of about 2.0 s. Use the SHM mode.
What is the period of a mass on a spring?
T = 2π√(m/k), where m is the mass and k the spring constant. A stiffer spring (larger k) or smaller mass gives a shorter period.
What is angular frequency?
ω = 2πf, the rate of phase change in radians per second. It appears in the wave equation y = A·sin(kx − ωt) and in SHM.
What is the wavenumber?
k = 2π/λ, the spatial analogue of angular frequency — radians of phase per metre. Larger k means a shorter wavelength.