A hypothetical compound tuning fork illustrates how complex vibrations decompose into sine waves

Evidence

This principle—that the sum of the solutions is the same as the solution of the sum of the sine waves— is called superposition and is a powerful aspect of the Fourier approach. — David Howard, Jamie Angus, coustics and Psychoacoustics, 439 (#corroborates, via linked claim)

Categorization

• XREF: connects to: Linear superposition lets separate vibrations coexist independently while interfering in shared space; Sinusoidal vibration is the fundamental atom of all sound; Any complex waveform can be decomposed into simple sine waves (+4 more)

Related

• Any complex waveform can be decomposed into simple sine waves (similarity 0.91)
• Sine waves are fully described by amplitude, frequency, and phase (similarity 0.91)
• Superposition lets complex waveforms be solved as sums of sine wave solutions (similarity 0.87)
• Linear superposition lets separate vibrations coexist independently while interfering in shared space (similarity 0.86)
• Any complex waveform can be built from independent orthogonal sine waves (similarity 0.85)
• All complex sounds, including noise, are superpositions of pure sinusoids (similarity 0.85)
• Any complex tone is decomposable into sine wave components displayed as a spectrum (similarity 0.82)
• Sinusoidal vibration is the fundamental atom of all sound (similarity 0.81)
• Any waveform can be approximated by summing orthogonal sine waves (similarity 0.80)
• Any waveform can be exactly modeled by combining sine waves (similarity 0.80)
• Fourier analysis recovers constituent sinusoids from any summed waveform (similarity 0.79)
• Superposed vibrations produce a net displacement that is the sum of the individual sinusoids (similarity 0.79)
• Sine waves of varying frequency, amplitude, and phase can construct any waveform (similarity 0.79)
• A sum of sinusoids is periodic only if their frequencies share a common divisor (similarity 0.78)

Broader Connections

• Any complex waveform can be decomposed into simple sine waves #corroborates (0.95)
• Superposition lets complex waveforms be solved as sums of sine wave solutions #corroborates (0.90) — David Howard, Jamie Angus, coustics and Psychoacoustics, 439