At-home STEM Activities: Calculating the Speed of Light with a Microwave Oven
This week’s Distance Learning offerings are focusing on optics, light, and the electromagnetic spectrum.
Light is an interesting form of energy, since it travels as both a wave and a particle. Today, we’ll focus on how it moves as a wave.
Image via Western Reserve Public Media
As said in Tuesday’s Distance Learning Module, the electromagnetic spectrum is a way of arranging all the types of electromagnetic radiation according to their wavelength. This type of energy is called radiation because it radiates, or moves away from, its source, and in an unenclosed area, a wave will keep moving at the same frequency—think about when you drop a pebble in a still body of water; ripples will radiate from the pebble all across the water. These are called traveling waves.
Here, the waves travel with no restriction. Animation via space.com; NOAA
But if we put our wave in an enclosed space, it’s going to act differently—think about our pebble again: when the ripples hit the edge of the water they bounce back. Waves in a bounded area will reflect back on themselves, and the resulting wave looks different; it looks like it’s standing still, hence it’s called a standing wave.
Animation via NOAA
Here, the blue wave travels to the right, bounces back, and travels to the left as the red wave. The blue and red waves interacting result in the standing black wave. The red points, where the black wave has no motion, are called nodes. The lowest amount of energy is at the nodes. The highest and lowest points on the wave (exactly half-way between two nodes) are called the anti-nodes, and these are the points of the most energy. For the activity we do below, you don’t need to know too much more about standing wave, but if you’re interested in learning more, Khan Academy has a great video about them.
A lot of things in physics have an application in our every day lives, and standing waves are no different! In fact, you probably have a machine that uses standing wave on your kitchen counter: a microwave oven. A microwave oven works by reflecting microwave radiation around the oven space, creating standing waves that zap energy into your food to heat it up. These microwaves travel really fast. In fact, they travel at the speed of light (as do all the other waves on the electromagnetic spectrum).
It took scientists a really long time to calculate the speed of light—up until 1676 when Danish astronomer Ole Rømer provided the first calculation, scientists weren’t even sure if the speed of light was a finite number. But a few hundred years later, we can calculate the speed of light using not much more than a microwave oven, a bar of chocolate, and a ruler. Let’s try it for ourselves!
Calculating the Speed of Light
Materials:
Microwave
Microwave-safe dishes (we needed both a plate and a bowl)
Chocolate bar
Ruler or measuring tape
Calculator
Instructions:
1. A microwave cooks food evenly by spinning it around so the waves can hit all parts of the food. For this activity, our goal is for only part of the chocolate to be hit by the microwaves, so we want to remove the spinning in our appliance. Most microwaves have a plate that spins around a center mechanism. Remove the oven’s plate and place a bowl over the mechanism to prevent your chocolate from spinning.
2. Put your bar of chocolate on a microwave-safe plate, and set it on top of the bowl in the microwave. We only want to soften the chocolate, so microwave it in short increments—we checked it every 5 seconds.
3. After about 20 seconds, our chocolate was soft enough to leave marks on the plate. Measure the distance between two of these chocolate spots—we’re doing science, so in centimeters, please! We measured a distance of about 6.1 cm.
4. Now for the calculations! We’ll need to know the frequency of microwaves that our ovens use. This information can often be found on the back or inside the oven.
This information was right inside the door of our microwave—2450 MHz. One MegaHertz (MHz) is equal to 1,000,000 Hertz (Hz). We need our frequency in Hz, so multiply 2450 MHz by 1,000,000 to get 2,450,000,000 Hz.
Now let’s return to the distance between the melted chocolate spots. The melted spots are the areas that received the most energy, i.e. where the anti-nodes are. To find the wavelength, we want to know the distance between two anti-nodes. We measured between two melted spots to get 6.1 cm. To get the wavelength, multiply 6.1 cm by 2 to get 12.2 cm. We want wavelength in meters, so if we divide 12.2 by 100 (since there are 100 cm in one meter) we get that the wavelength is 0.122 m.
Our goal is to calculate the speed of light, which is measured in meters per second (m/s). Hertz, the unit for frequency, is the name we give to inverse seconds, or 1/(seconds). Wavelength is measured in meters, so if we multiply the wavelength by the frequency we have:
So to calculate the speed of light, we just need to multiply frequency by wavelength:
So how’d we do?
The exact value of speed of light is defined as 299,792,458 m/s. If we find the percent error to see how far off we were:
That’s a pretty good calculation for using a microwave oven and chocolate bar! Our good work probably deserves a reward, maybe a few squares of a bar of chocolate.
