Standing wave simulator
A standing wave forms when waves travelling in opposite directions superpose. For an ideal string with fixed ends, allowed wavelengths are 2L/n and frequencies are nv/(2L). Nodes remain still while antinodes oscillate.
Standing waves
Fixed endpoints allow discrete modes. Increasing the mode number adds nodes. This is an ideal string model.
y(x,t) = A sin(nπx/L) cos(2πft)Ideal frequency for a 2 m string: 30.0 Hz. Animation is slowed to make the mode visible.
OpenStax · Standing waves and resonance ↗These are numerical illustrations. Exported values are simulation data, separate from the published human-study data in the research library.
Try this
Change the mode number. Count the antinodes and notice the fixed endpoints. Higher modes create more nodes and higher frequencies for the same string length and wave speed.
What the model leaves out
The model uses a two-metre ideal string and a fixed wave speed. It omits stiffness, frequency-dependent losses, and real string materials.
Where the equation comes from
Fixed endpoints allow discrete modes. Increasing the mode number adds nodes. This is an ideal string model.
OpenStax · Standing waves and resonance ↗