From Sparks to Waves: Analyzing Lightning and Thunder

Driving Phenomenon: Have you ever watched a thunderstorm and noticed that you see the flash of lightning before you hear the boom of thunder? Why does this happen, and how can we use mathematics to explain it?

In this task, you will use the From Sparks to Waves Simulation to investigate the properties of electromagnetic waves (light) and mechanical waves (sound). You will collect data and use mathematical models to support a claim about how wave speed depends on the type of wave and the medium it travels through.

Part 1: Engage (Anchoring Phenomenon)

  1. Open the simulation and ensure you are in the Propagation Model view.
  2. Observe the propagation of the light wave and the sound wave.

Q1: Describe your observations. Which wave travels faster away from the source? How does this explain why we see lightning before we hear thunder?

Part 2: Explore (Simulation Investigation)

Switch to the Oscilloscope Model using the button at the top. Here, you can adjust the frequency of both a Light (Transverse) wave and a Sound (Longitudinal) wave.

  1. Light Waves: Adjust the Frequency ($f$) slider for Light to three different values. Record the Frequency, Wavelength ($\lambda$), and Speed ($v$) in the data table below. (Note: 1 THz = $10^{12}$ Hz, 1 nm = $10^{-9}$ m. Be sure to use standard units or scientific notation for your calculations).
  2. Sound Waves: Adjust the Frequency ($f$) slider for Sound to three different values (the slider range is 20-200 Hz). Record the data.

Data Table: Wave Properties

Wave Type Frequency, $f$ (Hz) Wavelength, $\lambda$ (m) Calculated Speed, $v = f\lambda$ (m/s) Observed Speed from Sim (m/s)
Light        
Light        
Light        
Sound        
Sound        
Sound        

Part 3: Explain (Sensemaking)

Q2: Calculate the speed of each wave using the mathematical relationship $v = f\lambda$. Show one sample calculation for light and one for sound. Does your calculated speed match the observed speed in the simulation?

Q3: For a given type of wave (e.g., light in a vacuum, or sound in air), what happens to the wavelength as the frequency increases? Express this relationship in terms of cause and effect based on the formula $v = f\lambda$.

Part 4: Elaborate/Evaluate (Argumentation & Modeling)

Q4: Make a Claim: Based on your mathematical models and evidence from the simulation, make a claim about whether the speed of a wave depends on its frequency, or if it depends on the type of wave/medium. Support your claim with specific data points from your table.

Teacher Notes & Alignment **Targeted NGSS Performance Expectation:** HS-PS4-1 * **Science and Engineering Practice (SEP):** Using Mathematics and Computational Thinking. Students use the mathematical representation $v = f\lambda$ to describe and support claims about wave behavior. * **Disciplinary Core Idea (DCI):** PS4.A: Wave Properties. Students demonstrate that wavelength and frequency are related by the speed of travel, which depends on the type of wave and medium. * **Crosscutting Concept (CCC):** Cause and Effect. Students differentiate between cause and correlation, identifying that changing the type of wave changes the speed, while changing frequency causes a change in wavelength but not speed. **Evidence Statements & Student Work:** 1. **Representation (1.a.i, 1.a.ii):** Students identify and record mathematical values for $f$, $\lambda$, and $v$, and identify the relationship $v = f\lambda$ (Data Table and Q2). 2. **Mathematical Modeling (2.a, 2.b):** Students calculate the product of $f$ and $\lambda$ to show it is a constant for a given wave type, representing wave speed. They show that wave speed changes when the type of wave changes from light to sound (Data Table and Q2). 3. **Analysis (3.a, 3.b):** Students use $v = f\lambda$ to assess claims and distinguish cause and effect, explaining that changing frequency affects wavelength but not the constant speed of the wave in that medium (Q3 and Q4). **Implementation Tips:** * **Time:** 45-60 minutes. * **Materials:** Internet-connected devices, simulation link, calculators. * Ensure students are comfortable converting THz to Hz and nm to meters for accurate calculation of the speed of light ($3 \times 10^8$ m/s). * **Extension Options:** Challenge advanced students to research the speed of sound in water vs. air and use the simulation's concepts to explain why the speed changes.