SWBAT to compare sounds through the application of their understanding of scientific notation and exponents.

Sounds are often measured on a logarithmic decibel scale and are a perfect context for an investigation into exponents and scientific notation

10 minutes

This is a lesson about how we measure sound on the decibel scale. I start off by playing sounds that my students would recognize. I like to use this NY Times interactive sound timeline.

I could simply scroll through the timeline and listen to all the sounds with the kids, but I scroll past the ones with beer or bars. Its not that kids don't pass the bars each day, but I prefer to not spend my time in class discussing alcohol and bars and all the other things they see 10,000 times a day.

After we browse the timeline, I ask them to write down some of the most annoying sounds they have ever heard.

I could play this interesting radio story and show the related NY Times article on the impact and purposeful use of sound by people and industries in New York, but I like to show selected comments from other people in New York City. I like to show these first, because they are funny and remind everyone that they are not alone in their struggles with super annoying sounds. Here is one of the funny comments I like to use. The rest are in the resources for this section.

Then we take a few minutes sharing our personal experiences. I like to write these on the board to keep track of our common experiences with sound in New York City.

5 minutes

In preparation for this activity I print out the images included in this lesson's resources and laminate 8 sets of them for the 8 groups in my class. I give the class 5 minutes to put the images in order from quietest to loudest. Then I ask them to guess at the decibel level for each image. The one reference I give them is that conversation happens at about 60 decibels.

Many groups will ask questions like "how far away are we?" I address these questions by first asking them to sort as much as they can, assuming that each measurement is taken at an average decibel reading. If they need more information on a few images, I give them the distances to help. If students are really concerned, I write the distances on the board or on the back of the laminated cards.

25 minutes

I review the correct order of each sound with students. They follow along with this hand out: Decibel Question Sheet.docx The idea is that they can fill in the chart as I display the pictures in the correct order. I also grab sounds from free sound for effect.

Its usually at this point when there is some debate. *Somewhere *in this list will be serious disagreement (which is really healthy). This is the moment to make sure everyone agrees that distance is key, and furthermore, that these are simply average measurements. So there is healthy room for disagree.

I often explain the Doppler Effect by *showing* it. I just search You Tube for a passing train (preferably from New York City for my students). Something like this video would work. I show them the video and ask, "what did you notice about the sound level of the train?"

When we fill in the sound levels, students are surprised how different these levels are from their initial guesses. This is because they are usually thinking additively or multiplicatively, but this is *logarithmic*. They need to think exponentially here.

The question of the loudest possible sound ever often comes up. Its approximately 194 decibels in air (higher levels are simply shockwaves and cannot be heard). The key to understanding this limit is the idea that sound is a wave that vibrates both the air and your ears. This phenomena has a physical limit.

Next we look at the power levels. I give them this handout and ask them to use it figure out the pattern: Sound Power Chart.docx. I give the students time to work this out and solve the questions on the original hand out: Decibel Question Sheet.docx

**Note**: I leave the Cello and Trombone out of the final list because the range is so great, but it is a good talking point.

**Note 2**: If coordinating all these images and sounds feels like too much, use this CDC interactive site. You could print out the names of objects and have students order those. Then you could show the sounds with each link:

http://www.cdc.gov/niosh/topics/noise/noisemeter_flash/noiseMeter.swf

This site also does something similar:

http://www.nidcd.nih.gov/health/education/decibel/pages/decibel.aspx

Here is a third possibility:

http://www.dangerousdecibels.org/virtualexhibit/3howloudistooloud.html

20 minutes

The goal of this segment of the class is to help students master the exponential pattern in the power levels.

0 dB = 1 power

10 dB = 10 power

20 dB = 100 power

30 dB = 1000 power

I want students to first realize that an increase of 10 decibels multiplies the power by 10.

Next, I have them tackle a function for power based on decibels:

power(dB) = 10^(dB/10)

Students have fun seeing how many more times powerful one sound is than another. This spirals back to fluency over the laws of exponents.

The really difficult part of this approach is looking at increases of 5 decibels. I was careful to save this for the end. Students will think an increase in 5 decibels will increase power by half of 10, but it increases the power by the square root of 10. So here we have another opportunity to spiral back to square roots.

This lesson has so much to unpack. If you can't finish it all at once, spread it out over two days. Math is essential in understanding sound. You could even extend this to hearing loss or damage with earbuds.