Month: August 2025

26 August

Displacement-distance graph and displacement-time graph of a wave

Seng Kwang Tan AI, IP3 08 General Wave Properties, Simulations 0 Comments
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Exploring Wave Properties Through Interactive Simulations

One of the most powerful ways to learn about waves is not just by reading definitions, but by seeing them in action. This simulation allows you to adjust amplitude, frequency, wavelength, and speed and watch how the wave’s behavior changes over time and space.

By the end of this activity, you should be able to:

  1. Define and use the terms speed, frequency, wavelength, period, and amplitude, and connect them to what you see on the graphs.
  2. Recall and apply the relationship $v = f \lambda$ to new situations and solve related problems.

How to Interact With the Simulation

Two Graphs, Two Perspectives

  • The top graph (Displacement vs Distance) shows the shape of the wave along space at a single instant.
  • The bottom graph (Displacement vs Time) shows how a single particle moves up and down as time passes.

Controls

  • Use the sliders to change Amplitude, Frequency, Wave Speed, and Wavelength.
  • Press Start Animation to see the wave move. Press it again to stop.
  • Press Reset to return to default values.

What happens when you…

  • Increase Amplitude → The wave gets taller, but the speed and wavelength stay the same.
  • Increase Frequency → More oscillations appear in the same time, and the particle on the time graph moves faster up and down.
  • Change Wavelength → The distance between crests and troughs changes on the distance graph.
  • Change Speed → The wave travels faster across the distance graph.

Use these questions as you experiment with the sliders:

Amplitude

  • How does increasing amplitude affect the wave’s appearance on both graphs?
  • Does amplitude change the wave speed?

Frequency and Period

  • Observe the bottom graph: How many oscillations occur in one second when frequency is 1 Hz? What is the period (time for one cycle)?
  • What happens to the period when you double the frequency?

Wavelength

  • On the top graph, how do the positions of the crests and troughs change as you adjust the wavelength slider?
  • Can you measure one wavelength directly from the graph?

Wave Speed Relationship

  • Try setting frequency = 2 Hz and wavelength = 150 mm. What is the predicted wave speed using $v = f \lambda$
  • Now observe the simulation: Does the wave move across the distance graph at that speed?
  • Repeat for another set of values (e.g. f=0.5 Hz, λ=300 mm). Does the relationship still hold?

Connecting Both Graphs

  • Watch the red dot on the distance graph (a fixed point on the medium). How does its motion compare with the displacement–time graph?
  • Why does the red dot’s vertical motion look like a sine wave over time?
24 August

Simulation on Radioactive Decay using Dice

Seng Kwang Tan AI, IP4 19 Nuclear Physics, Radioactivity, Simulations 0 Comments

A simulation based on the casting of dice can be used to demonstrate the concept of half-life. Imagine a certain number of dice being cast together. All the dice that show a six are removed from the population. The remainder are cast again repeatedly, and each time, those that show a six are removed.

The question posed to students is : around which cast will the number of dice be reduced to half the original?

Here is the simulation:

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01 August

Lens Ray Diagram Simulation

Seng Kwang Tan IP3 07 Light, Simulations 0 Comments

I initially wanted to modify my GeoGebra applet on the converging lens ray diagram to include the case for infinitely far objects but thought I should give Claude.ai a try to generate one using javascript. It went very smooth. I merely took a screenshot of the original GeoGebra applet for reference, and used the following prompts: “Refer to this geogebra applet and make a html5 version. The user can change the focal length, the lens position and object height using mouse clicks or touchscreen drags. Keep the size responsive. Keep the buttons as overlays.” There were a few iterations after that but the first iteration was already good enough as a minimum-viable product.

This is the screenshot of the original applet that was used as reference by Claude.ai.

This is the end product:

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Access the full version here.