Vector Diagrams of Phase Difference

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Vector representations of phase difference. At A, waves X and Y are in phase. At B, X leads Y by 90°. At C, X and Y are 180° out of phase. At D, X lags Y by 90°. Time is represented by counterclockwise motion of both vectors at a constant angular speed.

If a sine wave X leads a sine wave Y by some number of degrees, then the two waves can be drawn as vectors, with vector X being that number of angular degrees counterclockwise from vector Y. If a sine wave X lags a sine wave Y by some number of degrees, then X appears to point in a direction that is clockwise from Y by that number of angular degrees. If two waves are in phase coincidence, then their vectors point in exactly the same direction. If two waves are in phase opposition, then their vectors point in exactly opposite directions.

The drawings of Above figure show four phase relationships between two sine waves X and Y. At A, X is in phase with Y. At B, X leads Y by 90°. At C, X and Y are 180° apart in phase. At D, X lags Y by 90°. In all of these examples, think of the vectors rotating counterclockwise as time passes, but always maintaining the same angle with respect to each other, and always staying at the same lengths. If the frequency in hertz is f, then the pair of vectors rotates together, counterclockwise, at an angular speed of f, expressed in complete 360° revolutions per second.