ToolsSound, propagation & hearing
Phase ↔ time ↔ frequency
Convert a time delay into phase at a frequency, and into path length or samples.
ms
°
cm
smp
Hz
°C
Phase wrapped to 0–360°
180°
Sum of two equal signals at this phase
−∞dB
This delay cancels (equal levels) at
100 Hz, 300 Hz, 500 Hz, 700 Hz, …
A fixed delay is a phase shift that grows with frequency. Inverting polarity is a 180° shift at every frequency. A delay t puts every odd multiple of 1/(2t) into phase opposition: 1 ms gives 500 Hz, 1.5 kHz, 2.5 kHz and so on, with full agreement at 1 kHz, 2 kHz, … (a comb filter). No delay matches a polarity inversion at all frequencies.
How it works
A time offset between two signals is a phase difference that increases with frequency. Use this to align subwoofers with tops, or to see at which frequency two arrivals cancel.
Formulas
- φ = 360° · f · Δt
- Δt = φ / (360° · f)
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