When you were very small, you probably asked a lot of questions: “How tall am I?” “Can you see me from there?” “Are we at Grandma’s house yet?” At that age, your measurement standards were things that were familiar to you. We often still use objects (artifacts) as measuring tools in our everyday life. We think of distance and mass in terms of familiar things like the time it takes to travel or how far we can see. But, of course, these references can change. For measurements that must be truly accurate, we need to use standards.

In this activity, you’ll explore how you could use the speed of sound and the speed of light as standards to measure distance, and decide which has the potential to be most accurate.

Materials:

Procedure I:

• • Access to the sound and lighting of a thunderstorm (from a safe place) or this video: Video - Thunder and lightning storm
  • Stopwatch
  • Sound recording or analysis software like Audacity

Procedure II:

• • Large flat chocolate bar Chocolate chips are not pure chocolate and will not work
  • Microwave
  • Ruler
  • Plate with raised edges, so that it can be inverted over the rotor in the microwave and won’t turn

Safety Notes: 

• Do not stay outside during a storm.
• Never eat in a laboratory.
   

Procedure I: Measuring with Sound

Every time we measure, we are comparing what we observe to some standard. We might use sound or light and might express a distance as kilometers or parsecs. We don’t need the high level of accuracy of a physicist or a medical professional, but we can use familiar experiences as analogies to help us understand the challenges of measurement.

Imagine you are on a sailing ship and a storm is in the distance. You want to estimate how far away the storm is by timing the difference between when you see the lightning and when you hear the thunder. Here’s a low-tech method sailors might use:

• After they saw a flash of lightning, they would count the number of seconds until they heard thunder.
• They would have estimated that for every 5 seconds, the storm was one mile away.

Why does this method work? Think: What is the difference between the speed of sound and the speed of light? The speed of sound varies with temperature and humidity, but is always significantly less than the (constant) speed of light.

Watch the video. 

Use the most accurate timer you can to estimate the distance to the storm. Create a chart:

1.  Is the storm approaching or moving away? Moving away
2.  Does the speed of sound vary based on temperature or humidity changes in the storm? Yes, sound varies to a far greater degree than light.
    

Analyze:

1. What limits your ability to get a good measurement? Your senses and changes in the speed of sound.
2. Is your timing tool good enough to measure changes from one strike to another?
3. What problems might exist using sound as a measurement standard? Sound varies with temperature and humidity, and it bounces off objects.
4. Is the speed of sound a constant? No, sound is a physical vibration, and cannot be transmitted unless there is a medium. The medium determines the speed. 

Procedure II: Measuring with Light

Electromagnetic waves (light light and microwaves) all travel at the same speed—about 299,702,547 m/s in air (299,792,458 m/s in a vacuum). One form of wave, the microwave, is used in our kitchen appliances.

A microwave oven uses microwaves to energize water molecules. The waves are released from both sides of the oven. At various points (nodes) they overlap, creating hotter areas inside the oven.

1. The hertz (symbol: Hz) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second. It is named after physicist Heinrich Rudolf Hertz. If your microwave is a standard model, it will have a frequency of 2.45 gigahertz. This means that microwaves move up and down 2.45 billion times per second. Check-in your microwave manual if you're not sure of the frequency of your machine.
2. Divide the speed of light by the wavelength of your microwave. Then divide it in half. That’s because the wave hits the surface twice.
   
   • wavelength = speed of light / frequency
   • This will tell you the distance that should exist between two hot spots in your microwave. These are the places on your chocolate bar that will melt first. Make a prediction.
3. Now take the revolving platform out of the oven. We don’t want the chocolate to rotate. Place a plate over the revolving mechanism. Set the chocolate bar on it carefully with the longer side facing you. Microwave just a little! Start with 5-second bursts. Watch carefully. As soon as you see melt lines, stop and measure.
4. As you calculate, be sure to watch the decimal places. You are measuring in centimeters; the constants are defined in meters.
5. How close was your prediction? Sample distance: about 6.1 cm 

Analyze:

1. The constant (speed of light) and wavelength of the oven (hertz) are defined in billions. The ruler you use is marked in centimeters and millimeters. What does this tell you about accuracy and significant figures in this model?  It is not possible to make a more accurate prediction due to the difference in magnitude.
2. Compare measurements that use sound with measurements that use the speed of light. What are the factors that affect accuracy? Your ruler is not remotely precise enough. The chocolate melts around the specific hotline.
3. In ocean studies we use sonar (measuring with sound) and lidar (measuring with light) to find undersea objects.

1. Which is the most precise? Lidar is more precise because of the wavelength.
2. What are the advantages of each? Sound varies with the medium. Light has a shorter wavelength.  

Conclusion:

What have you learned? The speed of light is a reliable constant for measuring distance.

What more do you want to learn?

Journal It:

Someone asks: “Where are you?” How do you answer? That may depend!

Imagine each of the following people asking you that question. Compose a one-sentence answer. Then look carefully at the terms that you use in the answer. Does the item include a reference to a standard or unit of measurement? If so, be very specific about what that standard or unit is. One possibility for an answer to the first question is included.