9.5.1 Phase Relationship

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. A quarter-cycle coreesponds to 90° or π/2 rad. So on and forth.

These four oscillations are in-phase with one another (phase difference of 0, 2π, 4 π, …)

The 1st and the 3rd are complete out-of-phase (phase difference of π, 3π, 5 π, …) with the 2nd and the 4th.

Each oscillation lags the one on the left a quarter-cycle (π/2 rad).

Each oscillation lags the one on the left 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. 😛

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.

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