MusicReasonProduction, Synthesis, and Audio Math
What phase does this time offset represent?
Declare a frequency and either a time offset or a phase in degrees. This tool converts between the two using the exact relationship between frequency, time, and phase rotation. It does not model filter phase response, waveform correlation, or whether a given phase relationship will sound like audible cancellation.
Answer
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Understand
The same time offset represents a different phase rotation at every different frequency, because phase is measured in fractions of a cycle and a cycle's own duration changes with frequency. A 1 ms delay is a small fraction of a cycle at 100 Hz but a full 360-degree rotation at 1000 Hz, which is exactly why phase relationships are always stated relative to a specific frequency, never in isolation.
Worked examples
At 1 kHz, a 1 ms time offset is exactly one full period, 360 degrees of rotation, which normalizes back to a displayed 0 degrees since a full cycle returns to the same phase. A time offset of exactly zero is always zero degrees, at any frequency.
Method and limitations
The raw phase in degrees is 360 × frequency × time (seconds); the displayed value normalizes that raw figure into the range -180 to +180 degrees, since phase repeats every 360 degrees and a normalized value is easier to compare across different time offsets. The inverse direction solves the same formula for time given a stated phase. This tool computes pure sinusoidal phase rotation only; it does not model a real filter's frequency-dependent phase response or predict whether a given relationship will sound like audible comb filtering or cancellation on program material.
The normalized display range of -180 to +180 degrees means a raw rotation of, say, 270 degrees is shown as -90 degrees instead, the equivalent shorter rotation in the opposite direction; both describe the identical phase relationship, since rotating 270 degrees forward lands in the same place as rotating 90 degrees backward. The cycle-count figure preserves the unnormalized information for anyone who specifically needs to know how many full periods the time offset actually spans, not just the final resting phase.