Parameters
Display Toggles
Presets i
Data
Math
Theory
Live Measurements
Wave Speed (v)0.0 m/s
Wavelength (λ)0.0 m
Frequency (f)0.0 Hz
Period (T)0.0 s
Harmonic (n)—
ResonanceNo
Wave Speed
$$ v = \sqrt{\frac{T}{\mu}} $$
Speed depends on Tension ($T$) and linear mass density ($\mu$).
Standing Waves
$$ f_n = \frac{n \cdot v}{2L} $$
Resonant frequencies occur when multiples of half-wavelengths fit exactly into length $L$.
Wave Equation (PDE)
$$ \frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2} $$
Modeled using finite difference method with discrete grid points.
Superposition
Standing waves form when an incident wave and its reflection interfere. Nodes are points of destructive interference (no movement), while antinodes are points of constructive interference (maximum movement).
Boundaries
Fixed: Reflects with a phase shift of $\pi$ (inverted).
Free: Reflects with no phase shift.
Open: Absorbs the wave (no reflection).
Free: Reflects with no phase shift.
Open: Absorbs the wave (no reflection).