More About the Domino Effect

Editor,

In his letter in the 7 December 2007 The Citizen Scientist "Backscatter" department about Part I of "Measuring the Speed of the Domino Effect Using the Windows Sound Recorder" Jim Hannon wrote:

"It always amazes me how quickly someone wanting to analyze a signal dives into the frequency domain. From looking at the time domain plots it is clear there is not a lot of energy at the fundamental frequency of the clicks. This means the peak is going to be hard to spot in the frequency domain. It seems to me in this case a simple auto-correlation in the time domain would show a big peak at the click interval."

There are a number of reasons for early resort to the frequency domain in signal analysis. The main one of these is that the efficiency of the Fast Fourier Transform (FFT) algorithm is so great that operations which are time consuming in the time domain can be more efficiently executed in the frequency domain, even though there is an over head of at least one FFT if not an FFT-IFFT pair.

Thus, we can compare an n point autocorrelation in the time domain with the equivalent process in the frequency domain. A single point of the autocorrelation requires about n multiplies and adds, so the operation count for m points of the autocorrelation is m(2n). To compute the entire (circular) auto correlation in the frequency domain requires one FFT (operations count ~4n log_2(n)) to get us there plus 4n (real) multiplies, so the total operations count (assuming we don't return to the time domain) is: ~n(4log_2(n)+4). I don't need to count the operations for an inverse FFT here as we a peak in the spectrum will give us the same information as a peak in the autocorrelation. Now we can make this specific; suppose n=1024, then if m>~20 then the frequency domain calculation requires fewer operations. Of course this analysis is approximate, and the real timings will depend on the efficiency of the actual FFT code used. I am sure I have missed a number of operations in the frequency domain operations budget, but the general principle remains; using the frequency domain we have a process of time complexity n log(n) compared to a time domain complexity of nm, and usually the values of n and m leave the analysis strongly in favor of the frequency domain method.

A second reason, and in practice more compelling, is that the code to do the processing in the frequency domain is just lying around on our systems, while the time domain processing will require more hand fettling of software.

Finally, while there may not be a lot of energy in the impulse train we are interested in, what is important is how much energy there is in the analysis cell containing what we are trying to detect compared to the neighboring analysis cells (whether we are working in the time or frequency domain is irrelevant here). Traditionally we require a post processing signal-to-noise ratio of more than 10dB, and often much more than this. Despite this, the energy in the signal that we are detecting is many dB below the energy in the signal plus interference (be it internal or external in origin).

Ron Larham

Readers, be sure to read Ron's two articles on the domino effect (Part 1 and Part 2). They are a classic illustration of an analytical study performed with readily available equipment. Editor.

Digital Sound Recording

Editor,

The articles in the December 2007 The Citizen Scientist on the domino effect and digital cameras got me to thinking about another digital tool that would be useful for amateur scientists. That is a way to record sounds. It turns out that some brands and models of MP3 players also have a microphone or input jack to record audio signals. The MP3 player I have would have been ideal for recording things like the sound of the dominos falling. It has no amplitude compression and stores the audio as a .wav file.

Jim Hannon

Comments and Questions

Editor,

1) I appreciated your editorial on the value of a digital camera to the amateur--but for reasons of domestic tranquility. I hate to throw anything away that may be useful in some future experiment, and I especially don't like to get rid of some gadget or apparatus I have made (unless I can give it away). This creates two problems for me: I clutter up all my living spaces, and I have trouble taking components from one experiment to use in another. Your digital camera idea saves the day! I just take a picture of the gadget or apparatus and place it into my notebook. Then I have much less trouble discarding or disassembling the things that clutter the house and office. (This is much appreciated by my supportive wife.)

2) I wonder if someone could tell me if there is any significant advantage to the vibrating reed electrometer in experiments as opposed to one of the modern high-end op amps. Can (or should) the two approaches be combined for a better measuring instrument?

3) I know that Dr. Carlson indicated when SAS was first formed that he didn't want to include amateur cosmology due to the crazy stuff that sometimes comes with it. However, I do have a couple of cosmology questions, and I hope someone can direct me to a few answers. Nevertheless, if cosmological things are considered out-of-line for SAS I will have no problem if no one wants to deal with it. (Simply let me know.) I also realize that these may be rather naive questions, too.

A) It is now known that the universe is not only expanding from the original Big Bang, but that it's expansion is accelerating. My question is why is it necessary to invoke a theoretical force called"Dark Energy" when there has never been any evidence for a fifth force and the existing theories provide no way to experimentally test the idea. I realize that I may be quite naive in this, but it would seem closer to Occum's razor to propose that it must be a gravitational phenomenon. For example, perhaps the primordial atom was larger than we think (not a singularity), and only the interior exploded, and there is a massive outer shell that has never been terribly hot expanding out into the universe. Whatever its history, it would be a huge mass just beyond the furthest quasars we can see. After an explosion, a mass like that would expand at a uniform velocity, but it's mass would still exert a gravitational effect on the visible mass behind it. Since a gravitational field accelerates objects it would cause an accelerating expansion for the visible universe on the inside of that sphere of matter. Perhaps we could eventually get an idea of the mass from the rate of acceleration.

B) Related to the last question, isn't it possible to explain the missing mass of the visible universe with something other than "dark matter?" I have read that most astronomers believe it exists, but despite my efforts, I haven't found much about why they think this instead of some more common substances. (I admit that I my search so far has only been in astronomy resources for the layman).

As usual, keep up the good work!

Thank-you!

Tim Kraemer

Tim, thanks for your comments. As for articles about cosmology, Shawn and I are in agreement that we need to stay away from purely theoretical articles on the subject, for we haven't the time to adequately review them and some that we have received are certainly, shall we say, off base. However, we have published some intriguing project articles that cover theoretical ideas. We were very open to the project articles by Lance Osadchey and C. Michael Edwards on measuring the absolute motion of the Earth, and this topic has generated more than 41 comments and 1,325 views (the record number to date) on the SAS Forum. We published these articles because they were based on experiments that other could replicate, not speculation. You can find these articles by entering the author's names in the search box at the SAS web site. Please consider posting your cosmological questions at the SAS Forum. Editor.

Best regards,

Dry versus Damp Cold

Editor,

I have a basic question about humidity and comfort.

I once heard a joke where three Texans are discussing the weather where they live: Amarillo, San Antonio, and Waco. They all say the weather isn't bad where they live: Amarillo has a dry kind of cold, San Antonio has a dry kind of heat, and, the punchline, Waco has a dry kind of rain. If I were crafting the joke, I would have chosen Houston as the wet region.

Anyway, people do speak of certain regions not feeling so cold because "it's a dry kind of cold." A member of my commuter van pool visited Colorado at Thanksgiving and commented that it wasn't bad because it was a "dry cold."

I started wondering about this because I know that we add moisture in our home to make the air feel warmer at a given temperature, thus saving money on our heating bill when set to ~ 70 F.

At higher summertime temperatures, moisture evaporates from your skin if the air has low moisture content. Thus, because of the heat removed from your body by the evaporating water, at the same temperature you'll feel much more comfortable in a dry place (Tucson) than in a damp place (Houston).

So, the rule "dryer is cooler" rule holds at 70 F and at, say, 105 F. Do the rules change at lower temperatures?

If cold, dry air feels warmer than cold, damp air, what is the explanation? Does (cold) moisture condense on the skin under certain conditions, thus cooling us more efficiently than cold, drier air?

Maybe you already have an explanation for this or can debunk what people say about the advantage of "cold, dry weather." If not, you may post my questions in "Backscatter."

Thanks,

Jeffrey Bledsoe

Readers, what do you think? Send your comments and links to web sites that address this question here. Editor.

More About Damselflies

Editor,

With your picture of two damselflies mating, the text mentions that the male stays with the female, as she lays eggs, in order to protect her. Not so! He holds on to her to prevent her from mating with another male, thus ensuring that it's his sperm, and only his sperm, that fertilizes her eggs, and therefore, his DNA that is passed on.

Tom Gartner

The damselflies in the photo are not mating. Instead, the male is holding the female behind her neck to escort her as she deposits eggs along the edge of a pond. This protects the female from the advances of other males. The males of this species play a very active role in the egg laying process as they lead their mate to various sites where she deposits eggs. At the pond in the photograph, dozens of coupled pairs were engaged in egg laying. Editor.

Another Non-Profit Online Library

Editor,

I wanted to let you know about ReadPrint.com. It's a massive non-profit library similar to Bartleby, except it's far better organized and user friendly. We've been using it extensively in school. It's great for doing research since you can search within the books.

Warm regards,

Jennifer

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