A juggler may not understand the mathematical representation of phase, but they are using the effect as they throw balls in the air at different times.

It is important to understand the concept of phase before starting the Waves section. In short: a full wave cycle consists of 2π radians.

Key Concepts

The oscillations of two pendula can be represented by two sine or cosine curves. If the pendulums don't swing at the same time, the curves will not be together and instead will be separated by an angle φ. This is called the phase difference or phase angle.

A phase angle of π means that the pendula are completely out of phase (antiphase), whereas phase angles of 0 or 2π make the pendula oscillate in phase.


Pendulum pattern

Pendula in a line, each swinging at a slightly different frequency, will go in and out of phase with one another.

Rotating vectors 

A little bit extra for those who are interested: phase difference can be represented with rotating vectors.

Test Yourself

Use quizzes to practise application of theory.


Exam-style Questions

Online tutorials to help you solve original problems