Real instruments are chains of coupled vibrating bodies. A plucked string transfers energy into a soundboard. A clarinet reed drives an air column. Each coupling changes the sound in ways neither component could produce alone.
The coupling chain
Energy flows through a series of coupled resonators. The output of each stage becomes the input to the next. The coupling strength controls how much energy transfers between stages.
Excitationpluck / bow
→
Resonator 1string
→
Resonator 2soundboard
→
Outputair radiation
Resonator 1 alone
Resonator 2 alone
Combined output
Coupling strength
The coupling strength sets how much of the first resonator's output drives the second. Weak coupling: the string dominates and the body barely contributes. Strong coupling: the body reshapes the character completely.
40 %
220 Hz
180 Hz
Why coupling matters
Energy transfer. When resonator 1 (string) vibrates, it pushes against resonator 2 (soundboard). The soundboard absorbs some of this energy and re-radiates it at its own resonant frequencies. This is why a guitar string sounds thin without the body — the body amplifies by absorbing string energy and radiating it more efficiently into the air.
Pitch pulling. When two coupled resonators have similar natural frequencies, they pull each other toward a common frequency. This is used deliberately in piano design — the soundboard's resonances are placed to reinforce certain notes. It's also responsible for wolf tones in cellos, where coupling becomes so strong that the string's pitch destabilises.
Feedback loops. In self-sustained instruments (clarinet, violin, flute), the resonator's output feeds back into the excitation. The reed or bow continues adding energy only when the feedback is in phase. This is what makes these instruments sustain indefinitely — they are active feedback systems, not just passive resonators.