Category: Uncategorized

Why is it when I sit in my office alone at work I don’t feel alone? People stop by once in a while, but not that often…. Now that Becka is working at the Textile Center, I am alone in the house when I work at home. I work at home on Thursdays so I can make it to the health sciences orchestra rehearsal at 5:00. Home is a lot closer to the U of M than work. The upside is that I can blast Niel Young at full volume and Becka doesn’t scream bloody murder… Oh well, I’ve got a mocha and a Lucy to keep me company…

This weekend Danielle and I rode our bikes along the “Grand Rounds” — a string of parks in Minneapolis that are connected by biking trails. We covered 25 miles in two and a half hours. We took the bike path along the new light-rail track back from Minnehaha Creek Trail up to Washington Ave near the MetroDome. The train passed by a few times, and at one point I noticed the Doppler Effect as I biked past a ringing warning light.
You normally think of the doppler effect as a change in the pitch of a sound when the source of the sound passes you. For example the vrooom sound of the Indy 500, or an ambulance siren. But it also happens when you are the one moving and the source of the sound is stationary.
When the distance between the sound source and the listener is getting smaller, the pitch will sound higher to the listener. When the two are moving apart the pitch will sound lower.
You can train yourself to recognize musical intervals. For example, if you hum the first two pitches of “Somewhere Over the Rainbow”, you have an interval called an “octave”. The first interval of Beethoven’s 5th symphony is a “Major Third”. The first interval of the James Bond Theme “For Your Eyes Only” is a “Major Fifth”. The major third, major fifth and octave correspond to frequency multipliers of approximately 1.25, 1.5 and 2.
If you passed right by a continuous tone on your bicycle, and recognized that the pitch changed by, for example, a Major Third, could you deduce how fast you were traveling?
Suppose the tone was a A 440. That means 440 waves would hit your ear each second. As you approach the tone, you would hear a B 494 and after you passed it you would hear G 392. To alter a pitch from 440 to 494 means that you would travel the distance that 54 A 440 waves occupy in one second (the 54 that you hit while you travel plus the 440 that moved towards you would add up to the 494 that you observed). 54 A 440 waves occupy a distance of (340.29 meters per second divided by 440 per second * 54 = ) 41 meters. 41 meters per second is 91 miles per hour.

Sorry to hit you all with this again, but I have updated a few calculations and made some interesting new observations.
A friend sent me a link to a website with an interesting new material called liquid metal. They have a video of a steel ball bearing bouncing on a plate of this metal, which shows the material’s surprising elasticity. The steel ball bounces for much longer than on a similar plate of titanium or steel.
The bouncing sound was somewhat like a metronome. Except that I noticed that the time it took for the ball to bounce got shorter the longer it bounced. So it starts out going ping — ping — ping — ping quite regularly but after a while it is faster, ping — ping — ping — and eventually is bouncing so quickly it sounds like a buzzing noise.
The ball bearing appears to be behaving as an oscillating spring with a decay. But what kind of decay? Was curious.
So I found an application called Wire Tap Pro” which has a 30 day free trial. I recorded the audio track of the bouncing ball bearing and opened it in sound studio.

I took a few data points from the audio track. I selected an interval of ten bounces, and sampled about every five seconds through the 40 second recording. I added one last point at the end at the best resolution I could discern (it got hard to read because the bounces got quieter and closer together).
I typed the data into a text file using my favorite text editor, vim.

 1  start   end
 2  0.134   2.635
 3  4.969   7.146
 4  9.956   11.813
 5  15.180  16.695
 6  19.969  21.211
 7  25.043  25.957
 8  29.986  30.613
 9  34.982  35.291
10  36.424  36.637

What I really wanted to plot was the time since ball was released on the X axis, and duration of the bounce on the Y. So I needed to plot the average of the start and end time versus the average of the duration. I used perl, my digital swiss army knife, to convert this file.

1  perl -pi.bak -e 's[([\d.]+)\t([\d.]+)][($1+$2)/2.0 . "\t" . ($2 - $1)/10.0]e;s/start/time/;s/end/duration/;' bounce.dat

This resulted in converted data:

1  1.3845  0.2501
2  6.0575  0.2177
3  10.8845 0.1857
4  15.9375 0.1515
5  20.59   0.1242
6  25.5    0.0914000000000001
7  30.2995 0.0626999999999999
8  35.1365 0.0308999999999998
9  36.5305 0.0213000000000001

This I could plot using GNUPlot and this plot file:

set term postscript eps color 48;
set output "test.eps";
set size 3.2,5.2;
set origin 0,0;
set multiplot;
set size 3,5;
set origin 0.1,0.1;
set pointsize 20;
set xlabel "time since release (s)";
set ylabel "duration (s)";
f(x) = a*x + b
fit f(x) '/Users/arahn/bounce.dat' via a,b
set xtic rotate by -45;
set title "Bouncing Of a Steel Ball Bearing";
plot f(x),'/Users/arahn/bounce.dat' with points pt 7 ps 3 ti "liquid metal";

To get this pretty graph:

gnuplot also gave me the regression values, intercept of 0.256846 s and slope of -0.00645081 s/s. This means that each bounce lasts 99.354919% as long as the bounces in the previous second. I was amazed at how well the data fit the regression line!
I would expect that decay would act on the total energy of the system — but we’ve shown that it correlated with the duration of the bounce. However, the tricky part is that you can’t really draw any conclusion based on how the duration of the bounce correlates with how long ago the ball was released. Energy is lost when the ball strikes the ground. As time goes on, it is striking the plate more and more often. What I’d really like to do is correlate the how many times it has hit the ground with how much energy it has. My hypothesis is that it would be an exponential decay in energy with respect to each bounce.
To determine how many times the ball has hit the ground, we could count them all. Or we could use calculus. The integral of the rate (clicks per second) is a function determining how many clicks have passed at time t.

click duration = d = mx + b
click rate = 1 / d = 1 / (mx + b)
num clicks = N = integral ( 1/ (mx + b) ) evaluated from zero to t
N = ( ln( mt + b ) - ln( b ) ) / m

We can turn that around to find out how the duration of a click is related to the number of times the ball has bounced:

m N = ln( d ) - ln( b )
d = b em N

I went back to see if this new data jives. We expect the first click (index zero) to have a duration of b, or 0.257 seconds. The first bounce in the audio recording is 0.261 seconds. Here is a table comparing the actual bounce times versus expected:

1  hit_num actual_time computed_time
2  0   0.261   0.257
3  10  0.242   0.242
4  20  0.228   0.227
5  30  0.212   0.213
6  40  0.197   0.199

Outstanding! The numbers are almost identical. Before you berate me for whimping out after 40, keep in mind what a nuisance it is to try and count all the blips in the recording.
Let see, we also know that the click duration is equal to the velocity (in meters per second) divided by the acceleration of gravity (G). Thus

velocity = b G em N

Here my hypothesis is wrong : Energy is proportional to the square of velocity. But we’ve shown that the duration of each bounce is proportional to velocity, and therefore the square root of energy. This reveals something interesting about inelastic collisions that I didn’t realize before.
An experiment for next time: We’ve shown that the amount of energy lost each time the ball strikes the plate is proportional to how quickly the ball strikes the plate. I wonder if the amount of noise that it makes is proportional to either the speed, or the energy with which it strikes? We could use the same sound recording to look at the size of the sound wave and relate it to how closely together the clicks occur.

I sometimes wish I could travel back in time to when I was a child in the garden with a pumpkin.

I just wanted to share some oboe info. One thing was this: I just have to brag about my new oboe reed guillotine invention. You can buy one of these Reiger Tools for $150. Or you can spend a few hours with a router, drill, etc…

Also, the other day I bought some english horn reed supplies. English horn reeds are pretty similar to oboe reeds, but the guy at the store (Wes, who plays with the Metropolitan Symphony) gave me some info on the differences. I recopied it on a napkin during knitting yesterday:

I forgot to show on the diagram that the bottom of the tip begins at 51.5mm and probably goes up about a mm to 52.5. That leaves 3.5 mm or so for the tip. He also indicated that he prefers to rough in the back first, then let it dry over night. Then the next day work on the tip *dry* (is this crazy?) and then wet it, clip it open at 57mm, and tie on the wire. I’ve never consciously made a “front” and a “back” to my reeds before, but he said since the lower lip provides more cushion that the window should therefore be bigger (46mm instead of 45mm).
I’ll try my hand at English Horn reeds sometime soon, I’m sure. As if I didn’t have enough to do with my oboe and Brahms’ 4th, hee hee hee.

“Compared to the relative simplicity of the Polynesian sequences, the Welsh results were all over the place. There was no sign of a clear-cut distinction in Wales analogous to what we saw in Polynesia where two separate clusters were so clearly the result of a mixture of people from very different origins. It looked as if we had a small number of little clusters which were all quite closely related to each other, rather than two big clusters separated by a large number of mutations.”
“The Seven Daughters of Eve” by Bryan Sykes, page 123

Playing on the beach!

Overheard regarding the Gizzard Shad : “This is the only species of fish that has a gizzard, and so it must be the only fish decended from birds.” This is, of course, untrue. The Gizzard Shad’s gizzard is an adaptation of the normal fish stomach to function like a bird gizzard. This adaptation is an example of convergent evolution, in which multiple instances of a similar functionality evolves separately. Eyeballs with lenses on the edge of clamshells is another example.

I did an amusing back-of-the-envelope calculation on the drive home tonight. I didn’t actually have an envelope….
The days are getting longer! But how much longer does the day get each day? Let’s suppose that the periodicity of the day length is described by a sine wave. And lets suppose that where we live the shortest day in winter has eight hours of sunlight and the longest day in summer has 16 hours. Also, to keep things simple, lets say day 0 is an equinox, for example the upcoming Spring Equinox on March 21 (or is it March 20? it varies from year to year). Hmm, we’ll need some variables sprinkled in there — how about y for the length of the day and x for the day of the year. Therefore our assumption can be written this way:

The data from the navy indicates that the days are getting longer by just over three minutes each day. That is still a little bit lower than expected. I suppose maybe the length of the day is not exactly a sine wave, what with the earth being in an eliptical, not circular orbit and all…

Today I saw a manatee. Actually I saw over twenty manatees. They don’t like to be in the Gulf of Mexico when it is too cold (below 65° F). The gulf was 66 degrees today. I saw these manatees basking in the warm effluent from the Fort Meyers power plant cooling towers. The water from the towers is a balmy 81&deg F — just right for manatees.