🌊 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.
Worked example: a sound wave
A 256 Hz sound in air (v = 343 m/s) has wavelength λ = v/f ≈ 1.34 m, period T = 1/256 ≈ 3.9 ms, angular frequency ω = 2πf ≈ 1608 rad/s and wavenumber k = 2π/λ ≈ 4.69 rad/m.
What does the amplitude represent?
The maximum displacement from rest, the height of the wave’s peaks. It sets the wave’s intensity or loudness but does not change its speed, frequency or wavelength, which is why the plotted wave changes height without changing its horizontal spacing.
What is the difference between a transverse and a longitudinal wave?
In a transverse wave (light, or a wave on a string) the medium moves perpendicular to the direction of travel; in a longitudinal wave (sound) it moves back and forth along the direction of travel. Both still obey v = fλ.
What is simple harmonic motion?
Motion where the restoring force is proportional to the displacement, giving a sinusoidal oscillation. A pendulum (for small swings) and a mass on a spring are the two classic examples, each with its own period formula in the SHM mode.