Why do standing-wave-like patterns appear?

A continuous drive launches a wave that reflects from the far end. Incident and reflected waves of the same frequency interfere. With light damping and f near a resonance, the pattern can look nearly stationary (nodes and antinodes) even though the left end is driven, not fixed.

Where is tension T in this simulator?

On a real string, wave speed is c = √(T/μ). Here you set c directly (normalized L/s); raising tension or lowering linear density μ would increase c the same way. There is no separate T slider.

What do the harmonic presets and dashed node lines mean?

They mark the fixed–fixed spectrum fₙ = n c/(2L) with L = 1 — a common lab orientation guide. The left end here is driven, so true resonances differ slightly; use the presets as a sweep starting point, then fine-tune f and lower γ.

Fixed vs free far end?

Fixed: displacement stays zero at the right end (node, phase-inverting reflection). Free: a Neumann-style free end (antinode-like reflection). Switch the boundary and watch how the reflected wave changes.

Wave on a String

Shake one end, adjust frequency and amplitude. Standing waves and reflections.

About this model

Transverse waves on a driven string: the UI exposes wave speed c (from tension via c = √(T/μ)), drive frequency and amplitude, damping γ, and a fixed or free far end. Watch traveling waves, reflections, and near-standing patterns when damping is low and f is near a resonance guide.

Who it's for: Intro waves and sound; standing-wave labs and conceptual homework.

Key terms

transverse wave
standing wave
wavelength
wave speed
boundary conditions
damping

How it works

Discrete wave equation on a string with one driven end and a fixed or free far end. Adjust frequency and lower damping to see traveling pulses, reflections, and patterns resembling standing waves near fixed–fixed orientation frequencies.

Key equations

∂²y/∂t² = c² ∂²y/∂x² − γ ∂y/∂t

c = √(T/μ) on a real string (set c here). Fixed–fixed guide f₁ = c/(2L); left end is driven, so the spectrum differs — use f as a sweep knob and lower γ for standing-like patterns.

Frequently asked questions

Why do standing-wave-like patterns appear?: A continuous drive launches a wave that reflects from the far end. Incident and reflected waves of the same frequency interfere. With light damping and f near a resonance, the pattern can look nearly stationary (nodes and antinodes) even though the left end is driven, not fixed.
Where is tension T in this simulator?: On a real string, wave speed is c = √(T/μ). Here you set c directly (normalized L/s); raising tension or lowering linear density μ would increase c the same way. There is no separate T slider.
What do the harmonic presets and dashed node lines mean?: They mark the fixed–fixed spectrum fₙ = n c/(2L) with L = 1 — a common lab orientation guide. The left end here is driven, so true resonances differ slightly; use the presets as a sweep starting point, then fine-tune f and lower γ.
Fixed vs free far end?: Fixed: displacement stays zero at the right end (node, phase-inverting reflection). Free: a Neumann-style free end (antinode-like reflection). Switch the boundary and watch how the reflected wave changes.

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