Devansh Mittal
Devansh Mittal
Physics Educator and Mentor • Lead Developer
Generating Standing Waves on String (Resonance)
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Harmonic Frequencies & Physics Formulation Theory & Analysis
General Formula for the nth Harmonic:   fn = n · f1 = n · (v / 2L) = (n / 2L)√(T / μ)
For a string fixed at both ends (length L, tension T, linear mass density μ, and wave speed v):
• Fundamental Frequency (Default Configuration): f1 = 25 Hz (with L = 2.0 m, v = 100 m/s).
1st Harmonic (Fundamental): 25 Hz
2nd Harmonic (1st Overtone): 50 Hz
3rd Harmonic (Default Slider): 75 Hz
4th Harmonic (3rd Overtone): 100 Hz
5th Harmonic (4th Overtone): 125 Hz
6th Harmonic (5th Overtone): 150 Hz
7th Harmonic (6th Overtone): 175 Hz
nth Harmonic Frequency: n × 25 Hz
• Resonance occurs when the driving frequency f matches any of the integer multiple harmonics fn = n × 25 Hz, creating large amplitude standing waves with stationary nodes and antinodes. Dragging the right stand alters the string length L, dynamically adjusting all harmonic resonance frequencies in real time.