## September Lectures

Sept 2: Sect 1.1
Isolated fact, not related to physics of music: Blood pressure is usually measured in mm of Mercury. 760 mm Hg is one atmosphere, about 100kPa. So a unit of blood pressure is about 0.13 kPa.

Sept 4: Sect 1.2, begin 1.4.
Movies of the "pendulum waves" experiment. The song played during the experiment is by Tom Lehrer.

Sept 9: Definition of frequency f = 1/T.
Note to professionals: this is usually denoted not f but n (Greek letter "nu"), which we don;t use because it is almost indistinguishable from a v (scipt "vee"). More common is angular frequency w = 2pn, but we don't use that either   : )
Sect 1.3, resonance part of 1.4, including drawing and interpreting a resonance curve, which looks thus:

Amplitude of system response is plotted against frequency of driving force, for a constant amplitude of driving force. The solid curve is for greater damping of the system, the dotted curve corresponds to less damping. The resonance frequency is the frequency at which the response of the system is greatest.

Sept 11: More on resonance (sect 1.4), including the famous beaker breaker, about which we sometimes ask questions on exams;
Sect 1.5 (Lissajous figures) Your own Lissajous figure generator. You have to play around with this to get interesting figures. Try making the "interval between points" considerably smaller, then click "generate" to see the figure in motion. History of it;
bell in vacuum experiment.
Student question about heartbeat waveform: this can be seen here, but much of the detail of the wave is washed out. This shows 5 heartbeats, each consisting of two main burst of sound ("lub-dub"). More detail than you probably want.

Sep 16:   Bridge collapse (frames from movie). This site also refers to authorities saying that it was not resonance ...
Section 2.1. Important formula   v = lf   and equivalent versions such as   l = v/f. Here v is the wave speed called S = 345 m/s in the case of sound waves. "l" is the Greek letter lambda (and should appear as such in your browser, not as "l") and denotes the wavelength.
Here is an animattion of longitudinal and transverse waves (don't worry about the bottom two waves at this time). The longitudinal wave moves too fast to see the motion of the individual lines. That's better here.
If you are into Lissajous figures : the experiment shown last time will make it as a question of the week (a new one each week).

Sep 23:   Section 2.2 Reflection, Refraction, Interference; Section 2.3 Addition of Waves.
Wave addition. This allows you to add two arbitrary sine waves. Each wave is specified by an expression like A*sin(L*(x-f*t)) where A is the amplitude, L is the inverse of the wavelength, and f is the frequency. After you change the preset values (A = 2.5 etc), click on "change" to make that change take effect. To shift a wave by 180°, change the amplitude to its negative. To change phase by 90°, change the sin into a cos.

Sep 25:   Section 2.3, cont., Section 2.4 Beats. Interference from two speakers demo
Animation of pulses as in Fig 2-32. Another one lets YOU choose the wave shape.
You can see beats in the Wave Addition animation of Sep 23 by changing the frequency of one of the waves slightly. The frequency is the number given as 8.0 when you first open this link. Click just behind the 8.0, backspace to delete the 0, replace, say, by 1 (to read 2.5*sin(8.1*(x-1.0*t)) ) in one of the lines -- say, the g(t) -- and click on "change". That will give you a figure similar to 2-36, except with a higher frequency. Click on "forward" to see the wave move. Or, if you are lazy, just click on "linear dispersion - beats" (but then you won't know how to play around with it some more).
If you want to hear beats.

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