I am ending this week with one more music-related activity. This one is focused on sound and the ability of the human ear to ‘hear’ loudness and intensity, as measured in decibels. This, like in yesterday’s lesson, relates to the sine wave and transformations on the sine wave. I’ve adapted yet another activity from the Fostering Mathematical Thinking with Music, Casio 2015, where we look at the amplitude of a sine wave and compare it to the intensity of music. This should resonate with students since they listen to so much music and often times very loudly, so thinking about what their ears are doing to detect that increase in loudness, or intensity, hopefully is pretty engaging.
The activity begins with some interesting facts about the human ear, which I am including here – a little science along with the math:
“The human ear is truly an amazing piece of scientific measurement equipment. Besides helping to regulate the body’s balance and temperature, ears are designed to detect microscopic differences in clusters of air molecules.These are mostly pairs of nitrogen and oxygen atoms that are, on average, 3.7 Angstroms wide – 1/100,000th of the width of a human hair!
The ear measures whether pockets of these tiny particles have gotten bunched slightly more closely together, or spread slightly further apart. It can discern these differences to within one-BILLIONTH of a centimeter. Even more remarkable is that the ear is making these determinations as the pockets of air are arriving at somewhere between 20 and 20,000 times per second. Amazing! makes you want to stop and just listen for a moment, doesn’t it?” “Intensity and the Decibel Scale.” physicsclassroom.com., Physics Tutorial, n.d. Web. 3 Apr. 2014.
The activity, Amp Up the Intensity, is originally a graphing calculator activity that I converted into a ClassPad.net version. Students look at the sine wave and a transformation of the sine wave and compare these first. They then relate the sine wave to a sound wave and use a slider to see how amplitude and intensity are impacted by the coefficient A in y=Asin(x). They are then given examples of sound intensity from various objects (rustling leaves, vacuum cleaner, a jet taking off, etc.) measured in decibels, and compare these visually on a scatter plot and determine a regression that will model the relationship. The whole activity really focuses on how amplitude impacts the loudness.
Below are links to the ClassPad.net activity, a PDF of the original activity, which includes teacher notes and possible solutions to the questions, and a video overview of the ClassPad.net activity. Now, depending on which tool you have, you can work with either version of the activity.
- Amp Up the Intensity – Trig, Amplitude, Intensity & Loudness
- Amp Up The Intensity – Fostering Mathematical Thinking through Music
- Video Overview – CPnet Amp Up the Intensity – Trig, Amplitude, Intensity & Loudness
The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.
Remember – if you want to save and/or modify any of these activities, create a free account. Some useful links below:
- How to create a free ClassPad.net account (for anyone – students, parents, teachers)
- How to organize activities & share activities
- Some Ready-to-use activities that are already out there
- ClassPad.net YouTube Channel