A fixed time lag becomes a larger phase fraction when the waveform period gets shorter, so phase is a ratio of delay to period. The 3 s lag gives 1/4, 1/2, and 3/4 cycle for 12, 6, and 4 s periods exactly for the ideal periodic-signal model; real measurements add phase noise, jitter, bandwidth limits, waveform distortion, trigger uncertainty, temperature drift, and timing/phase measurement uncertainty.
Holding lag fixed makes phase grow as the period denominator shrinks. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A twelve-second period makes three seconds one quarter
With lag fixed at 3 seconds, period 12 seconds gives phase 1/4 cycle.
123=41 cycle
A six-second period makes the same lag one half
Keeping lag 3 seconds but shortening the period to 6 seconds gives phase 1/2 cycle.
63=21 cycle
A four-second period makes the same lag three quarters
With period 4 seconds, the same 3 second lag becomes phase 3/4 cycle.