Waves on a String — iLearnSTEM Labs

iLearnSTEM Labs

labs.ilearnstem.ca — Virtual Science Laboratories

Ontario Curriculum · Grades 9–12Beta

Waves on a Stringfixed–fixed

f 5.0 HzT 16 Nμ 10 g/mv 40.0 m/s

nearestf_1 = 5.00 Hzlocked ✓

λ8.00 mnode gap 4.00 m

v theory√(T/μ) = 40.0 m/s

v measuredf·λ = 40.0 m/s= theory ✓

Fixed — pulley · L = 4 m

RESONANCE — harmonic n = 1 · λ = 8.00 m · v = fλ = 40.0 m/s matches √(T/μ) ✓

Physics Lab 04 · Waves on a String — grid squares = 1 m · drag to orbit, scroll to zoom

Oscillator (driven end)

Driving frequency f5.0 Hz

tune onto a harmonic — the pattern locks in within ±2%

Drive amplitude2.0 cm

String

Tension T16 N

set by the hanging mass over the pulley

Linear density μ10 g/m

2 g/m ≈ fishing line · 6–10 g/m ≈ instrument strings · 16 g/m ≈ cord

v = √(T/μ) = 40.0 m/s

Far end

The far end is tied off over a pulley — a node at both ends. Every harmonic n = 1, 2, 3, … is allowed: f_n = n·v/(2L).

Display

Slow motion (8×)

Node markers

Amplitude envelope

Real strings vibrate too fast to watch — slow motion keeps every wave relationship intact while making the pattern visible.