## October Lectures

Sept 30: Section 2.2 Diffraction. The experiment described on pp 43/44 was shown,
Section 2.5, 2.6. Animated web pages with moving figures like 2.37 and 2-45 aboud, for example:
mouse waves (follow instructions in applet)
Doppler Adjust wave speed etc. by dragging on the arrow
another dopplerThis allows you to change the speed as the applet is running

Oct 2: Section 3.1. Photos of some of the standing waves shown in lecture.
You can make standing waves be addition of travelling waves in the wave addition applet: to get one of the waves to run to the left, change the - sign in the corresponding formula into a + sign, and click on "change". The frequency is determined by the number that is 8.0 when you start, the amplitude is the initial 2.5, and the wave speed the initial 1.0.
There is also lots on standing waves on the web, for example this.

Oct 7: Sections 3.2, 3.4 Table 3-2 and 3-7 contain the essential mathematical info from this lecture. If you remember f1 = v/2L for strings and open tubes (with v = S) which have all harmonics, f1 = S/4L for closed tubes, which have odd harmonics only, you can reconstruct all the information. To visualize: standing longitudinal waves

Oct 9: Section 3.4, continued, section 3.3.
Kundt's tube showed air motion and its nodes in a resonant tube.
Comparison of open and closed tubes. You can click on the image in the description.
The stroked aluminum rod shows longitudinal waves and interference.

Oct 14: Exam 1

Oct 16: Section 3.5, Chladni figures

Oct 21: Section 13.3, first 4 paragraphs, main qualitative points of sections 14.1, 14.3, section 9 as much as interests you, but here is a summary of the main point:
Recall the Overtone Series:
 n =     1 2 3 4 5 6 7 Interval: octave fifth fourth major third minor third augmented second? Ex: 110 220 330 (329.63) 440 550 (554.37) 660 (659.26) 770 (783.99)
The integer-related frequencies are heard without "beats"; but one cannot build a whole octave out of them for the following reason:
If "fifth - fourth = second" (one whole tone), then one whole tone should be (3/2)/(4/3) = 9/8 = 1.125, and an octave, which is 6 whole tones (5 whole tones and 2 half tones), would be (9/8)6 = 2.0273. But the octave should be exactly a factor of 2, anything else will sound worse than an equal percentage deviation in the other intervals. The Pythagorean scale uses 9/8 for all whole tones of the ordinary, major scale, but 256/243 for the half tones (between E and F, and between B and C). Because the whole tones are too large, the half tones must be too small, so that the overall scale comes out at a factor 2 for the octave. This means that the minor third (E-G or A-C) sounds flat (9/8 × 256/243 = 1.1852 rather than 6/5 = 1.2).
Another way to deal with this is to spread the error evenly, as in the well-tempered scale, in which one whole tone (major second) is a factor 1.12246... in frequency, because 1.122466 = 1.999... = 2

Oct 23: Section 4.1, 4.2. You can do your own synthesis of waves here. This will mainly show you that different wave shapes do correspond to different sounds. To synthesize a specific wave is a bit frustrating because the scales given are not correct (at least on my browser): what is labeled amplitude scale is really intensity, and the phase scale really goes between -100 and +100 degrees. And not only intensity, but in decibels. That means, say for a square wave, put the fundamental at 0 db (unit intensity), the third harmonic with amplitude 1/3 intensity 1/3² = 1/9 ~ 1/10 at -10 db, the fifth with amlitude 1/5, intensity 1/25 which is about -14 db and so on. After this was written I found several others that may have fewer harmonics and limited amplitudes (not db), but are much easier to use, for example this and that and one without sound where you can see the Gibbs phenomenon well, etc..
The description of Fourier analysis allows you to listen to various waves and their counterparts electronically generated from their spectra.

Oct 28: Sections 4.3, 4.4. The most impressive demo was the bottle band.

Oct 30: Section 4.4, p. 134 (filters). Here is another link to the web site on Fourier synthesis/analysis that was shown in lecture and is suggested in the current homework.