Strike two bells that sound identical – but one rings five seconds, the other fifteen. Same natural frequency, different damping. This quality factor is often the more diagnostic signal in acoustic material testing.

Q-factor mathematics

Q = f0 / Δf3dB

Δf3dB is the half-bandwidth – frequency difference where amplitude drops 3 dB. High Q (> 100) means sharp peaks; low Q (< 10) means broad ones.

Relation to damping

ζ = 1 / (2 · Q)

What influences damping?

  • Material: steel low damping (Q often > 1,000), rubber very high (Q < 5).
  • Internal cracks: friction surfaces drain energy – measurable damping rise.
  • Microstructure defects: porosity increases internal friction.
  • Heat treatment: properly tempered steel shows higher Q than misadjusted batches.

Diagnostic significance

Brake disc example:

  • Intact: Q ≈ 850 at mode 4.
  • 4 mm micro crack: Q drops to ≈ 620 (frequency shift < 5 Hz – in noise).
  • 8 mm crack: Q ≈ 380 (frequency shift 35 Hz – classically detectable).

Micro cracks not reliably detected by frequency alone become robustly detectable via Q.

Practical notes

  1. Q determination needs high frequency resolution.
  2. Below Q ~ 30: bandwidth exceeds mode spacing – use curve fitting (Lorentz).
  3. Q is temperature-dependent – include temperature variation in master build.