Standing Waves on a String

Find the harmonics

  1. Choose any of the three optional investigations above the apparatus. Read the question, make a prediction, then try it. You can freely explore all controls.
  2. Switch on the oscillator. Adjust the generator frequency until the string forms clear, large loops. Each resonance is a harmonic.
  3. Change the hanging mass, vibrating length, or string density. Explore how the resonance frequencies change. The harmonic buttons tune the generator exactly.
  4. Turn on Strobe lock to see the string at the same point in every cycle. This virtual synchronized light holds a stationary view without flashing the screen. Use the phase slider to inspect different positions. Track one string point to see transverse motion: it moves up and down, not along the string.
  5. Show nodes and antinodes at resonance. Nodes stay still; antinodes have the largest motion.
  6. Move the two measurement cursors using their sliders, or drag their handles along the ruler. The adjacent-node button aligns the cursors at resonance. The readout only converts spacing to wavelength when the cursors sit on neighboring nodes. Adjacent nodes are half a wavelength apart: λ = 2Δx.

Normal viewing shows slow motion so you can follow the vibration. The generator displays the physical frequency. No observations are saved.

Standing-wave apparatus

OSCILLATOR OFF

Why does this happen?

Adjust generator & string
VIBRATOR / PULLEY / MASS HANGERWAVES LABORATORY
Standing-wave lab benchA signal generator drives a mechanical vibrator. A string crosses a pulley and supports a hanging mass. A ruler and two movable cursors measure distances along the vibrating section.200 g30.0 HzFUNCTION GENERATORVIBRATORSTRING POINTVIBRATING STRINGPulleyMassZORNSCIENCE / WAVES & RESONANCESLOW MOTION · 1/40 SPEED
READY TO DRIVE THE STRING

Horizontal distances follow the ruler; vertical motion is magnified. On small screens, scroll the apparatus sideways.

● N · Node: stays still│ A · Antinode: greatest motionDashed envelope: limits of motion

Measure the string

Place A and B at neighboring nodes. Their separation is half a wavelength, not a full wavelength.

CURSOR SEPARATION

WAVE SPEED
FUNDAMENTAL f₁
NEAREST HARMONIC
RESONANCE

v = √(T/μ)   ·   fₙ = nv/(2L)   ·   λₙ = 2L/n

About this model

A lightly damped, small-amplitude string with ideal fixed ends and constant tension T = mg. The small driver is approximated as a node. Near resonance (within 0.5%), an ideal single harmonic makes nodes exactly stationary. Away from resonance, a modal sum (at least 16 modes, extended to cover the driving frequency; damping ratio 0.018) models the steady forced response; transients, pulley friction and string stretch are omitted. Away from resonance, several modes contribute and interior nodes are not stationary. Node markers appear only near resonance with the oscillator on and a nonzero drive. Changing length rescales the apparatus view; use ruler values rather than screen distances. The string’s vertical displacement is magnified; horizontal distances and ruler readings use the selected vibrating length. The strobe samples one phase per driving cycle without visible flashes. Normal playback is 1/40 speed and may alias at very low screen refresh rates.