As previously mentioned, I’m watching a little bit of Fringe in order to be able to talk sensibly about it later this week. I watch the Season 1 finale last night, and its treatment of parallel universes is about what I’d expect for tv, but being the obsessive dork I am, I got distracted from the big picture by a silly side issue.
There’s a running joke for the first bit of the episodes about Walter trying to find various pieces of scientific equipment, only to find that Peter has appropriated them for some sort of personal project. One of these items is an electron microscope (presumably an SEM, though the prop they dragged out later looked more like the TEM we used to have in the basement). Later, it’s revealed that the secret project is a device to digitize some of Walter’s old vinyl LP records, using the electron microscope to read the pattern in the grooves.
The device is used for a fairly ridiculous bit of magic CSI technobabble, but my immediate reaction was “Why would you need an electron microscope for that? That’s ridiculous overkill.”
But then again, part of being a physicist is always checking your immediate reactions, and this is an easy one to test quantitatively. So, would you really need an electron microscope to digitize an old LP?
The key question here is what resolution you would need to be able to faithfully reproduce the bumps in the record’s grooves, and work out the sound frequency. If the smallest bumps you would expect are small enough, then an electron microscope might be a reasonable choice for a readout device. So, how small are those bumps?
Well, the highest frequency of sound audible to humans is around 20 kHz. This is outside the bandwidth of a typical LP system (which is why, annoying audiophiles notwithstanding, CD’s are a better medium for music than LP’s), but good enough to put an upper limit on the resolution. So, if you imagined making a record that was just a steady 20kHz tone for the full playing time (it would not shock me to learn that some avant-garde composer tried this), the needle would be going over a peak every 0.00005 s.
How far does the record move in that time? Well, the rotation speed is 33-1/3 revolutions per minute, which we convert to the more scientific units of 3.5 radians per second. Multiply by 0.00005 seconds, and you find that the record turns through an angle of 0.000175 radians per oscillation of our 20kHz tone.
That doesn’t get us a size, yet, because the linear distance covered will depend on the radius at which we’re looking. A point on the outer edge of the record is moving considerably faster than a point in by the label. That means that the wave peaks will be spaced more widely at the outer edge than in toward the center. Since we’re looking for the smallest possible feature size that you might want to resolve, we want the inner edge, which has a radius of at least 5cm. Multiplying 0.000175 radians by 0.05m gives us a feature size of 0.00000875 m, or 8.75 microns.
Now, this is pretty small– roughly a tenth the thickness of a human hair– and people do use electron microscopes to take pictures of things at this scale. But this is also well within the resolution of an optical microscope, and remember, this is the absolute smallest feature you could possibly imagine needing to detect on a record. The vast majority of the sounds we care about would involve much, much larger features.
So, a little bit of math basically confirms my initial reaction: you could use an electron microscope to do it, but it would be massive overkill. It’d be much easier, and much cheaper, to use a laser or something to scan the grooves with conventional optics.
(This is the point where you remind me that I’m complaining about technical details of an episode whose premise involved people with drug-induced psychic powers blowing themselves up. To say nothing of creepy assassins trying to move between parallel universes. Which is true, as far as it goes, but this is how my brain works, and I can’t help it.)