Bad vibrations

A point I've made here more than once is that my doubting many claims of the paranormal isn't because I think it's necessarily impossible, but because our sensory-interpretive systems are so fundamentally flawed.

I mean, they work well enough, for most of us most of the time.  But not only do we have the capacity to miss a great deal of what's going on around us -- as the famous experiment in which a great many test subjects failed to notice a guy in a gorilla suit showed -- what we do sense is all too easy to misinterpret or remember incorrectly.  This is why if someone comes to me with a claim of some supernatural occurrence or another, I'm going to ask for some kind of hard, scientifically-admissible evidence.  To quote astrophysicist Neil deGrasse Tyson, "I need more than 'you saw it.'"  Neither he nor I are accusing anyone of lying or perpetrating a hoax; the problem is that eyewitness testimony is all bad, even if you mean well and are trying your hardest to be honest.

[Image is in the Public Domain]

To throw another monkey wrench into the situation, consider the recent paper by psychologist Rodney Schmaltz of MacEwan University.  Schmaltz became interested in the possible role of subsonic vibrations in claims of haunting; there was a case in England where a medical research building was claimed by several workers to be haunted, in one case by a "gray form that materialized, floated across the room, and vanished."  More than one person saw the apparition, and several described a sensation of chill, as if they were being watched.

The culprit turned out not to be a ghost, but a furnace fan that had set up a subsonic standing wave in the basement.  The frequency of the wave was around twelve Hertz -- so below the range humans can hear -- but created resonant vibrations in our eyes and ears that could be sensed by the brain.  The result: eerie hallucinations, altered perception, and feelings of unease.

What Schmaltz did was try to see if there was a way to measure the human response to infrasound, by setting up test subjects to listen to recordings of music through headphones.  Half the test subjects listened to calm instrumental music, and the other half eerie recordings that could have been the soundtracks of horror movies.  What the subjects didn't know, though, was that half of each of the audio tracks had been altered to include infrasound.

The results were incontrovertible.  The subjects exposed to infrasound weren't aware of it consciously, but responded to it regardless.  Also, it didn't matter what the audible component was.  If they were exposed to infrasound, they reported feeling unsettled and unhappy, and -- most strikingly -- a saliva test showed elevated levels of the stress hormone cortisol.

“Whether they were listening to calming instrumental music or something more unsettling, the infrasound shifted their mood and their stress response in a negative direction,” Schmaltz said.  “In plain terms, you cannot hear infrasound, but your body and your mood appear to respond to it anyway, and the response tends to be unpleasant.”

Schmaltz suggests that a lot of the reports of ghosts in old buildings might be nothing more than infrasound coming from antiquated boilers, furnaces, and plumbing -- aided, of course, by the fact that we're already primed to expect something paranormal from such places by a hundred years of scary movies set in run-down mansions.

Even knowing all of this, though, probably wouldn't make a whit of difference to our actual responses in such a situation.  Because that's the other part of the problem, isn't it?  Our emotional reaction to a particular set of circumstances has a way of derailing our higher brain functions, especially when that reaction is "OMG a ghost, run!"

And unfortunately, that applies not just to those Crazy Kids and Their Stupid Dog, but to skeptical rationalists.

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Pitch perfect

It's funny, sometimes, what we don't know.  I've played the flute for almost forty years -- started out self-taught (bad experience with elementary school band), then was lucky enough to study with a brilliant classical flutist named Margaret Vitus for five years when I lived in Seattle.  I've since played in three different bands and a community orchestra, and besides the classical repertoire, I've become fairly proficient in Celtic, English country dance, and Balkan music.

But it wasn't until the last band I was in, the trio Crooked Sixpence, that I actually figured out some peculiarities of my own instrument.  I was fortunate enough to play with Kathy Selby, who is not only a brilliant Celtic fiddler but a physicist (then teaching at Cornell University).  Kathy taught a class called "The Physics of Music," which combined her two areas of expertise -- and the class looked at, amongst other things, how specific instruments work.

So it seemed natural for me to ask her something that's always puzzled me; why flutes go sharp once they warm up.  The difference is greater (obviously) when it's cold out -- so the temperature increase the instrument experiences once I start playing it is bigger -- but it is noticeable even on a warm day.  On first glance, it seemed to make no sense.  Objects expand when they warm up, so (I thought) the thermal expansion would make the tube longer, and the pitch should drop, making it go flat.  That they actually go sharp seemed completely opposite to my intuition.

And of course, she immediately knew the answer; it's because sound travels faster in warm air.  Since the frequency of a wave is directly proportional to its velocity, if the sound wave is moving faster, its frequency goes up -- and so does its pitch.  The thermal expansion of the tube is minuscule, so any drop in pitch from the tube becoming longer is negligible.

I also found out from Kathy -- when I attended a free lecture on musical acoustics she gave -- why a bunch of different instruments playing the same note all sound different.  I knew that that the fundamental note (let's say it's A above middle C) has to have a wavelength that is the same length as the tube (or string, or whatever) of the instrument that's playing it.  A sound of that wavelength will set up a standing wave that then sets the air moving and projects outward toward the listener.

But a flute playing an A above middle C and a fiddle playing an A above middle C sound completely different.  The reason, I learned, is because there is more than one wavelength that fits a particular length:

[Image is licensed under the Creative Commons Allowed and forbidden standing waves, File:High School Chemistry.pdf, CK-12 Foundation]

The ones on the left "fit;" the ones on the right don't.  The top one on the left is the fundamental pitch.  The ones further down are called overtones, and that's the key to why instruments sound different.  The greater the number and amplitude of the overtones, the more the sound wave the instrument produces deviates from a simple sine curve.

Sound waveforms, top to bottom -- flute, piano, trumpet.  [Image from Doug Davis, 2002]

As you can see, flute tones are pretty simple, very close to a sine curve.  But look at the trumpet waveform.  Same fundamental pitch -- the peaks and troughs of the waveform line up with the flute's and the piano's -- but the shape is entirely different.  That's because of the number, and intensity, of the overtones.  (Instruments that have forced vibrations from a bow being dragged against the string, like violins and cellos, have a lot more overtones -- and thus more complex waveforms -- than instruments where a string is plucked or struck, like guitars and pianos.  The same comparison holds for double-reed wind instruments like oboes and bassoons, which produce way more complex sound waveforms than flutes do.)

The whole topic comes up because of a paper that was presented recently at the annual meeting of the American Physical Society, which contained the solution to a long-standing question in the physics of music; why do the pipes of an organ play a tone that is considerably lower pitched than the sound wave that should fit the length of the pipe?

Organ builders have known about this for over a hundred years; to get an organ pipe to sound the note you intend, you have to build it a little shorter than you'd expect.  (The "end correction" you have to use to make the pipe's pitch match what physics would predict from its length is equal to 0.6 times the radius of the pipe.)  But why?  Shouldn't a wave of that length be a little too long for the pipe, and be one of the "forbidden standing waves" shown on the right side of the first figure?

The key to the answer was discovered, quite by accident, by a Swiss organ builder named Bernhardt Edskes.  He was working on repairing an organ, and noticed that a tiny piece of gold plating had flaked off one of the pipes.  He only saw it because when he played that pipe, the flake floated above the top of the pipe.  But since there was air blowing up the pipe, why wasn't the flake completely blown away?

Leo van Hemmen, a physicist at the Technological University of Munich, realized that both the "end correction" question and Edskes's mysterious floating piece of gold were the result of the same phenomenon.  When an organ pipe is played, the rising column of air causes the formation of a stable vortex above the top of the pipe.  When van Hemmen used smoke to make the vortex visible, and its height turned out to be exactly 0.6 times the radius of the pipe, he knew he'd solved the puzzle.  The spinning cylinder of air creates a longer tube for the sound to resonate in -- so the wavelength of the lower-pitched note fits perfectly.

Humans have been making music for tens of thousands of years, and I find it fascinating that we are only now understanding the intricacies of what's going on inside the instruments we play.  It may be that we don't need to know the physics of music to enjoy it, but for me, it's fun to find out how complex these things are -- and that all As above middle C are not created equal.

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