One of my favorite moments in Scale is the New Geography (a very helpful teaching tool for leading Power of Ten workshops) is when Eames Demetrios in Some Tools for Teaching Scale is in the middle of describing an aspect of scale and an ice cream truck drives by with its chirping ice cream music in the background. Demetrios spontaneously uses this as example of comparing linear growth (which most of us are used to) vs. exponential growth (which is about scale and many of us are not as aware of).
The speed of the truck is moving linearly at a roughly constant speed on a road behind Demetrios who is seated in front of a building while the music from the truck is moving exponentially. What is the difference? It’s why the music on the moving ice cream truck sounds louder all of a sudden as it gets closer and passes behind Demetrios and the building. Sound travels about 300 m/s. (10+2) With a diagram, Demetrios explains the difference in the clip on the DVD.
Sound travels faster through water than air (almost 5 times faster) – which is about as fast as a speeding bullet! An example of sound and speed in a different way is to ponder - how does Superman do it? How does he get there in time to rescue the person? We know that he is faster than a speeding bullet which is 1,500 meters per second. (10+3) But how can he get there in time if he were in New York and the person calling for help is in Boston? It would take up to 15 minutes or almost 1,000 seconds (10+3) just for the sound of the person’ voice to reach Superman. And then another 200 seconds (10+2) for Superman to reach the person or about 3 1/2 minutes later! Or what if someone was in California? Then it would take the yell for help over 3 hours or 12,600 seconds (10+4) to get to Superman in New York and then about 45 minutes or 2,700 seconds (10+3) for Superman to reach the person.
A hat tip to Science Ray