This GeoGebra applet was modified from an existing applet to show the relationship between the pressure-distance and displacement-distance graph of a progressive longitudinal wave.
This is a 3D printed Pythagorean cup, otherwise known as a greedy cup, where if one pours far too much water or wine or whatever your greedy heart desires, all the contents in the cup will leak out through the bottom.
This is based on the design by “jsteuben” on Thingiverse (https://www.thingiverse.com/thing:123252). The siphoning effect kicks in when the water level is above the internal “tube” printed and hidden into the walls of the cup.
I printed another cup based on a more conventional design as well, but due to the wrong settings given when I prepared the gcode file, the cup was rather leaky when the water level was low. This design by “MonzaMakers” has a protruding siphon tube. (https://www.thingiverse.com/thing:562790)
Explaining how the siphon works is easier with the second cup. When the water level is lower than the highest point in the siphoning tube, it remains in the cup. When it exceeds the highest point of the tube, water begins to flow down the part of the tube leading to the opening at the bottom of the cup. The falling water column creates a suction effect and continuously draws the rest of the water in, until the cup is dry.
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:
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.
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 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.