Student groups create an analogy that accurately compares the speed of light in air to the speed of sound in air.

The speed of light in a vacuum is about 800,000 times faster than the speed of sound in air.

In lesson Wave Hello, students learned about the different wave properties, among them wave speed. Though we use wave speed throughout the unit, we have never directly explored the speed of light or how it compares to the speed of sound in air.

There is a common misconception among people that the speed of light is relatively close to the speed of sound. The truth is, in the Earth's atmosphere the speed of light is about 800,000 times faster than the speed of sound. This is tough to grasp without some kind of analogy, so students spend this period to create one. They research various quantities and develop an analogy along the lines of the speed of light is to the speed of sound as x is to y.

This applies NGSS Science Practice 1: Asking questions (for science) and defining problems (for engineering), Science Practice 5: Using mathematics and computational thinking, Science Practice 6: Constructing explanations (for science) and designing solutions (for engineering) and Science Practice 8: Obtaining, evaluating, and communicating information. It is in the context of performance standard HS-PS4-1: Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. CCSS Math Practice 1: Make sense of problems and persevere in solving them is also applicable for this activity as students first must understand the problem and then create an analogy that makes sense.

10 minutes

To have students think about how the speed of light compares to the speed of sound, I show a video, False Start, where a camera is positioned over 200 meters from the start line of a race. We see the runners begin to run before we hear the starters pistol. I ask the class: "Does this mean that every runner did a false start? What explains this?"

Students raise their hands and I call on one to provide the explanation that the sound wave takes time to reach the camera whereas the light takes no time at all. So this gives us an apparent delay between when we see the runners start and when we hear the pistol. I repeat back to the student their answer: There is a delay because sound takes time to reach us but light gets to us from the racers the moment they start the race. Then I ask a rhetorical question of the class: "Does light really reach us the instant an event happens, or does it just seem that way?" Today, we explore how the speed of light compares to the speed of sound.

I display the Speed of Light power point and instruct students to take notes on the information included in the slides. Throughout history there have been many attempts to measure the speed of light. I read this passage from the article on Wikipedia titled Speed of Light: "In 1638, Galileo proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. He was unable to distinguish whether light travel was instantaneous or not, but concluded that if it were not, it must nevertheless be extraordinarily rapid."

Then I display the diagram made by Rømer and read again from Wikipedia: "The first quantitative estimate of the speed of light was made in 1676 by Rømer (see Rømer's determination of the speed of light). From the observation that the periods of Jupiter's innermost moon Io appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it takes light 22 minutes to cross the diameter of Earth's orbit."

Astronomical distances were first used to determine an approximate speed that light travels. Many more clever experiments were carried out and now we are certain of the speed of light, which is just under 300 million meters per second. I finish the rest of the power point and then task the students with developing an analogy that compares the speed of light to the speed of sound in air.

35 minutes

Analogies are a powerful way to compare things. I tell the students that they have the next 35 minutes to create an analogy that compares the speed of light to the speed of sound. They work in groups of 2 and have access to the internet. Their task is to create an analogy with a set of objects that the typical person can comprehend; in addition, their analogy should be clever. For example, they should not do something like, "The speed of sound is to the speed of light as 1 dollar is to 800,000 dollars". Students should search out actual objects that give a good analogy to the speed. Also, their analogy can involve any types of units, among them size, speed, mass, and volume.

Students collect the Analogy Activity handout. They have two choices for their analogy, each group only needs to do one analogy. They can compare the speed of light to the speed of sound in air (first choice) or they can compare the visible light range to the total electromagnetic spectrum (second choice). The spectrum analogy is also useful because the visible light range is tiny compared to the overall spectrum.

First, students must make a ratio that compares the speed of light to the speed of sound or that compares the range of visible light to the total spectrum. Most groups work on the speed analogy; I am guessing this is because it is easier to calculate. Light travels about 800,000 times faster so they need to find two things that differ by a factor of 800,000. Students brainstorm different objects to compare. They use their smart phones, the classroom computers and textbooks to look up the value of various objects. I encourage groups to choose things that we can easily understand and perceive. For instance, they should avoid an analogy that uses some thing very small that we cannot conceive with our senses, such as an atom or bacteria. I redirect groups that attempt such analogies and tell them they can do better. While students work on this, I walk the classroom and give support where needed.

5 minutes

As the period nears the end, I collect the handout from each of the student groups. Then I use my document camera to view Student Work - Analogies (you may have to download this resource to see all of the student samples). Students are very clever and find some good analogies to compare the speed of light to the speed of sound. Some of my favorite include:

Speed of light is to the speed of sound as...

- 10 years is to 6 minutes
- The speed of a fighter jets is to the speed of a slug
- The speed of a rocket is to the speed of a three-toed sloth
- The height of Mount Everest is to the height of a pebble
- The height of the Empire State Building is to the thickness of a piece of paper
- The volume of an Olympic sized swimming pool is to a gallon of milk

We finish the class with a pretty good understanding that though light is not infinitely fast, it is much faster than the speed of sound.

There are so many aspects of this universe that we simply cannot perceive with our five senses or understand through life experience alone. The study of physics opens up the secrets of the universe and leads us to deeper understandings and technologies that otherwise would be impossible. It is my hope that I have given my students both an appreciation for the process of scientific exploration and the desire to go further in their knowledge of how nature operates.

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