We must be able to calculate the phase difference when the information is presented to us in graphs.

Displacement-Distance Graph

Sometimes you’re given a displacement-**distance** graph (like the one below) and asked to calculate the phase difference between two oscillations (at two different positions of the wave).

First, let’s agree that the oscillation at A **leads** the oscillation at B. How can we tell? Because the wave is coming from the left, meaning the wave will hit A first before B. The one further from the wave source must be lagging since it is the delayed version.

Now back to the calculation. The phase difference between 2 points on a wave depends on how far apart they are along the wave. The larger the separation Δ*x*, the larger the phase difference Δ*θ*. We know that if 2 points are one wavelength apart, the phase difference between them would be 2π rad. By simple proportion, if they are separated by a distance of Δ*x*, the phase difference Δ*θ* would be

Two Displacement-Time Graphs

Other times, you’re given the displacement-**time **graphs of two oscillations (see below), and asked to calculate the phase difference between them.

Firstly, let’s agree that A leads B. This is easy to tell since B is a delayed version of A. Whatever A did, B will do at a later time.

As for the calculation, you must first obtain the misalignment in time Δ*t* between the two oscillations. Just look for the delay between two crests, or two troughs, or any two corresponding points from each of the two graphs. Since a misalignment of one period corresponds to a phase difference of 2π rad, a misalignment of Δ*t* would correspond to phase difference of

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**Video Explanation**

How to Calculate Phase Difference from Graphs

**Concept Test**

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