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.
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:
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.
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.
I created a series of GeoGebra apps for the JC topics of Waves and Superposition, mainly on the concept of Phase Difference. The sizes of these GeoGebra apps are optimised for embedding into SLS. When I have time, I will create detailed instructions on how to create such apps. Meanwhile, feel free to use them.
Instructions on how to embed the apps into SLS can be found in the SLS user guide.
Phase difference between two particles on a progressive wave. Move the particles along the wave to see the value.
Phase difference between two particles on a stationary wave. Move the particles along the wave to observe how their velocities are different or similar.
Observe velocity vectors of multiple particles on a progressive wave.
In order to help students visualise a wavefront, a 3-D image is usually used to show the imaginary line joining particles in phase. I created the Geogebra apps below to allow students to change the wavefront and observe it move with time at a constant wave speed. There represent simplified versions of waves on a ripple tank with a linear and circular wavefront.