We can apply the concept of phase to any repetitive periodic motion. One complete cycle corresponds to 360° or 2π rad. Half-a-cycle corresponds to 180° or π rad. One and a quarter-cycle coreesponds to 450° or 5π/4 rad. So on and forth.

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See if you can recognize the phase differences among the following oscillations.

In-phase (phase difference of 0, 2π, 4 π, …)

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Complete Out-of-Phase (phase difference of π, 3π, 5 π, …)

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Quarter-cycle Phase Difference (Each oscillation leads the one on the right by π/2 rad)

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Each oscillation leads the one on the right by 1/8 of a cycle (45° or π/4 rad). The profiles of two progressive waves moving from left to right are now clearly visible. There is the transverse wave in the bobbing heads, and the longitudinal wave in the gyrating hips. 😛

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In an actual progressive wave, there is a continuous increasing phase lag in the direction of wave propagation. Each wave element lags the preceding wave element by a bit.