Chapter 7

Section 7.3

Try out this applet (custom-developed for this text by Andrew Cantino), which allows you to explore the normal modes of a beaded string, and helps you to understand why there is a minimum meaningful wavelength. (This is the applet used for problem 7.3.)

Read about recent research on ultrashort wavelength vibrations in solids, excited using 50 femtosecond laser pulses. (1 femtosecond = 10-15 seconds; a 50 femtosecond pulse would have a length that is only 15% of the diameter of a human hair!!)
A 100-picosecond laser pulse has created hot plasma at the surface of an aluminum target. The resulting shock wave can create vibrations with wavelengths on the order of the distance between atoms. Image courtesy of and © Prof. Ki-Yong Kim.

Section 7.4

You’ll definitely want to check out this absolutely jaw-dropping applet by Paul Falstad, which allows you to superpose modes of a beaded string, show the oscillations of each mode, listen to the resulting sound, add a driving force, show the decomposition of standing waves into left- and right-moving waves, and much more! Spend some time exploring all the different options.

Section 7.5

You may have already explored this applet by Paul Falstad in chapter 6, where we used it to illustrate systems of coupled oscillators with different masses, but it also works perfectly to illustrate longitudinal oscillations for systems with equal masses.

Section 7.6

Recent research on the auroral ionosphere (the part of the atmosphere responsible for northern lights) has shown that there is an unusual type of standing wave called a “lower hybrid solitary structure”, which explains some puzzling features of the “auroral hiss”, and advances our understanding of plasmas. Read more in this summary from Physical Review Focus.
Image courtesy of and © Dr. Peter Schuck

The Normal Modes song!