CBE 30355 - Lecture Notes - Aug. 24, 2023
Announcements
Class notes
Read through pages 17-25 of the notes and view the online narration below. Don't forget to complete the quiz in Canvas!
The main points of the lecture were
Goals:
After this class you should be able to:
- Know where the continuum hypothesis breaks down.
Reading
- The class notes.
- BS&L, chapter 1
Additional Readings:
In class we talked about the speed of sound. While we won't be doing much
acoustics in this class, it's a fun topic. While we usually think of sound propagating through air, in fact it is just as important how sound propagates through water - particularly if you are on a submarine! For just about everything you ever wanted to know about sound in the sea, visit the website
here. The history of underwater acoustics near the bottom of
this page is particularly fascinating.
Demonstration:
In class today we demonstrated bubbles - or actually anti-bubbles! An ordinary soap bubble is a thin film of soapy water surrounding a sphere of air, and floating around in the air. An anti-bubble is the exact reverse: a thin film of air surrounding a sphere of water and floating around in water. In order to make the anti-bubble last a bit longer we add a little bit of sugar to increase the density of the water inside the air sheath (so that it counterbalances the lower density of the thin air sheath) and thus is neutrally buoyant. From the density of this sugar solution (about 1.3 wt%) and anti-bubble size (2.9mm radius, 0.1ml volume), the thickness of the air sheath is only about 5µm!
A nice article describing how to make anti-bubbles by Kim and Stone is found here.
David.T.Leighton.1@nd.edu