Phase and Phase Difference

If two oscillations reach their maximum displacement at the same time, they are said to be in phase at that time (if they also have exactly the same frequency, they will remain in phase).

If one oscillation is at its maximum displacement when another is at its equilibrium position, the two oscillations are said to have a phase difference of one quarter of a time period (T/4).

For many oscillations (a pendulum, a mass on a spring etc) a graph of displacement, x against time, t is very similar to a graph of sine of angle against angle (). For this reason, phase differences are usually expressed in terms of angles rather than times.

For example, the two oscillations shown below are T/4 or /2rads or 90° out of phase with each other.

Similarly, the next diagram shows two oscillations which are T/2 or rads or 180° out of phase with each other (in this case we also use the term “in anti-phase”).

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