Friday, January 21, 2011

On Cars

I went on the corner of Memorial Dr. and Ames St. this morning and pointed the brightly colored cans at the cars. A friendly guy who's applying to Sloan for an MBA walked by (on his way, presumably) and chatted.

I wish I could the spectrogram program to output audio and stream the display at once (right now I can either have choppy audio and perfectly smooth display, or perfect audio and choppy display). Then I would have included the audio synchronized to the display in the video.

I don't think I can embed audio files, so here is the wave or the ogg.

Both in the specgram and in the audio file, I've filtered out everything above about 1kHz. I've also replicated the first half, but sped up by 2. This makes it easier to perceive the whale calls.

It'd be interesting to know why the frequency drops off like it does. The cars are not actually slowing down as they pass me by. Also, when you're on the train platform and you hear the "Eeeeeaaooo" (supposed to sound like a cat's meow without the 'm'), that's not purely because of the Doppler effect, because since the train is moving at a constant speed, the amount of Doppler shift would be constant.

Made in Inkscape

(I wish Blogger'd let me upload an svg.) So the speed actually observed as the car moves in and out of the antenna's range varies. For example, have the observation take place at the origin. As the car moves left, the observed speed decreases since less of the car's velocity lies in the direction of the measurement (the dotted line from the origin to the car). The moment the car passes the origin, this line is perpendicular and at this point the car appears instantaneously still. Let h=1. The ratio of the car's velocity that is in the direction of the dotted line is equal to the cosine of the angle a. sohcahtoa so cos(a) = x/sqrt(1+x^2)
WolframAlpha : y=x/sqrt(1+x^2)

Which looks (the positive part) similar to the way the frequency rolls off in our measurements (barring a reflection since time on the spectrogram is increasing right to left):

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