See: Radiolab’s Walls of Jericho podcast from October 2010.

Act 1: [mp3 | 8M] The hosts lay out the story of Jericho, where an Israelite army brought the walls down, supposedly by shofar (a ram’s horn) blasts. Along the way, we learn about the logarithmic decibel scale. In the final seconds of this clip, we get to the question that all my students were already asking: what would it really take?*

Act 2: [mp3 | 8M] Wherein David Lubman, the acoustical scientist consulted by the hosts, reveals how many shofar blowers it would take to bring down the walls.

Act 3: Continue playing the Act 2 file to explore issues of how to focus the sound and the physics of sound cannons.

*At this point, my kids set to the calculations. They wanted to know if there was a faster way. It was a beautiful experience where the kids asked me to take them from brute-force-arithmetic to honest-to-goddess upper level math. Then I hit play on Act 2. In the words of the experts in this podcast, “there’s a problem.” Just as my class noticed (and demanded we contact the Radiolab folks), another teacher noted a problem in Act 2’s big reveal:

Steven from Palo Alto

There appears to be an inconsistency with the explanation of the mathematics that leads to the total number of shofar players needed to me the 177dB target. If every time the number of shofar players is doubled, the dB level increases by three, then the number of shofar players would have to be doubled 29 times between 95 dB (the sound level of one shofar player) and 177dB. 2^29 shofar players is more than 1000x larger than the 407,380 figure that David Lubman gives. I am not trying to be critical, but I was hoping to use this story as an example of exponential growth for a class that I teach, and this is where my demonstration derails in relation to the podcast. Did anyone look as closely at this part of the story as I did?

Oct. 10 2010 07:50 PM
I have no idea how to reconcile this problem. Maybe there’s value in getting indignant that your answer is “wrong” — my students drafted a response to the Radiolab folks right there on the spot.

Georgia Performance Standards
(you would not believe how many people read my posts after searching a state standard — leave a comment if you’re one of them)
Physics
SP4d. Students will analyze the properties and applications of waves. Demonstrate the transfer of energy through different mediums by mechanical waves.
Mathematics II
MM2A2d and MM2A2e. Students will explore exponential functions. d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology. e. Understand and use basic exponential functions as models of real phenomena.
Mathematics III
MM3A2. Students will explore logarithmic functions as inverses of exponential functions.