Phase Difference

The first of two apps on Phase Difference allows for interaction to demonstrate the oscillation of two different particles along the same wave with a variable phase difference.

The second shows two waves also with a phase difference.

In both cases, the phase difference $\Delta\phi$ can be calculated with

$$\Delta\phi = \dfrac{\Delta x}{\lambda} \times 2\pi$$

where $\Delta x$ is the horizontal distance between the two particles or the horizontal distance between the two adjacent identical particles (one from each wave) and $\lambda$ is the wavelength of the waves.

Longitudinal and Transverse Waves

I modified Tom Walsh’s original GeoGebra app to add a single oscillating particle for students to observe the direction of oscillation, as well as to optimise it for the Student Learning Space.

You can choose to shift the particle that you want to focus on.

The app can also be used to show how the displacement of a particle in a longitudinal wave can be mapped onto a sinusoidal function, similar to the shape of a transverse wave. For example. a displacement of the particle to the right can be represented by a positive displacement value on the displacement-distance graph.

Here is an animated gif for those who prefer to insert it into a powerpoint slideshow instead:

Animation of longitudinal wave and transverse wave

This is the original app:

The good thing about GeoGebra apps is that everything is open-source – free for anyone to edit. Being able to read the “source code” or rather, the mathematical syntax used by others, I have learnt a lot. For example, I learnt how to use Sequences from this original app to generate oscillating lines with different phases.

Movement of Particle in a Wave

This GeoGebra app allows students to observe closely the movement of a particle in a progressive wave, with two possible directions of energy propagation.

In a typical question, students will be asked to predict the next movement of a particle given that a wave is moving left or right. Usually, students will need to imagine the waveform shifting slightly to the left or right in order to figure that out. This app follows the same visualisation technique to identify the subsequent movement of any particle along a wave.

Invisible Spheres using Hydrogel

I used this demonstration to start a conversation about refractive index with my IP3 kids. These hydrogels certainly generated a lot of excitement as the kids were fascinated with how invisible it becomes when placed in water.

You can get a 1000 (yes, one thousand!) of these for $1.29 at Shopee. Make sure to choose the transparent ones instead of the coloured version when checking out.

Say goodbye to the messy demonstration involving the soaking of glass in a beaker of vegetable oil or glycerin.