S04E12: The Bus Pants Utilization

I was afraid while this week’s episode was taped.   I feared everyone on set would ask me how a theremin works.   And I had not done my homework.  In case this ever happens to you, read on, and I will spare you the embarrassment.

This week, Sheldon played his theremin, the eerie sounding electronic instrument favored by avant-guard musicians:  from the Beach Boys to Vladimir Illyich Lenin.   The theremin came to Lenin shortly after Soviet scientists developed a proximity sensor.


Just like Sheldon, Lenin enjoyed playing the theremin.

The key to a Theremin is a so-called “tank circuit”.   In a classical theremin you will find a coil of wire connected to two metal plates.  The coil of wire is sometimes called a “choke”. That’s because it does not allow  fast-changing signals (“high frequencies”) to pass through.    The two metal plates are called together a capacitor, because of their capacity to hold opposite electric charges on each plate.   Their reservoirs of charge allows fast signals to pass through, but are quickly depleted by slow-changing signals (“low frequencies”).  The parallel plates work in exactly the opposite sense as the coil.  One element blocks low frequencies, and the other blocks high frequencies.   Putting the two together allows only a narrow range of frequencies pass through.  Energy in the circuit sloshes around, between the charge on the capacitor and the current in the coil at a well calculable rate.

The specific frequency passed by the tank circuit depends sensitively on the values of the capacity of the parallel plates to hold charge (its “capacitance”) and the inability of the coil to change its current (somewhat opaquely called its “inductance”).   Every body and everybody has inductance and capacitance.  If we connect our tank circuit to an antenna you can change the resonant frequency by simply moving your hand near it, adding your own capacitance and inductance to the circuit and changing its tune.

A "coil" and two parallel plates (a "capacitor") form the heart of a theremin.

When you play a classical theremin, you don’t control the audio frequencies directly.  Our ears can only hear thousands of vibrations per second.   That’s fairly slow for electronics, and the size of the coils and parallel plates would have to be enormous.   It is much easier to build electronics working at higher frequencies.  So, theremin designers make use of a mathematical trick.   It turns out to be easy to find the differences between frequencies.  So by comparing two “tank circuits”, one you are modifying with your hand, and one without your intervention.  The frequency difference is sent to the theremin speaker.

Working off the difference is a common trick.  Your AM radio (if you still have one) has a tuner, but you are not tuning the tank circuit. Rather, you are tuning another circuit, close to the frequency you want to receive. Your radio uses the difference to find the signal.   Scrabble players take note;  this fancy trick is called superheterodyning.

The key here is the changing signals.   When physicists want to talk about the changes of values, rather than the values themselves, they need to work with differences, also called “differentials”.  The equations describing them are called “differential equations”.  Differential equations are key to understanding the flow of currents in the tank circuit of a theremin.   And the solving of differential equations was of course the main point of tonight’s story.

Unlike many other types of equations, there is no definite method to solve a differential equation.  Often physicists are led to try a few tricks, look them up in dusty old tomes, or ultimately to guess.  In modern times, we can enter the equation into a computer and hope it can find the answer.  Leonard had the brilliant idea this week to skip that step, and have the iPhone app recognize the handwritten equation and solve it directly.

Common differential equations have names.  The solution to the tank circuit is a “sine” function.   The “spherical Hankel function” mentioned tonight comes up when solving vibrations of spheres.   The laws of  population growth give a differential equation solved by “exponential functions” which is, unfortunately for us, the fastest growing of all the elementary functions.

I’m no iPhone designer, and the white boards were a salient part of the story this week.  Luckily we found a friend-of-a-friend of mine, Robert McNally who designs iPhone apps for a major online dating company.  Everything you see in this weeks show is 100% real, quality, iPhone development @%^#!.  Click on his name above, and you will learn a little of the inside story of the dueling app software.

Anyway, nobody liked my other iPhone app idea.  I want to make a Geiger counter with an iPhone.  I think it could work.  Just look for single bit errors in the iPhone memory due to ionizing radiation.  The error rate is proportional to the radiation.

So now they are out there.  Two good ideas for iPhone apps.  Elves, the shoemaker is waiting.

21 Responses to “S04E12: The Bus Pants Utilization”

  1. iPhone Apps on The Big Bang Theory « Ironwolf Says:

    […] app aspect of things here to my blog, and I would be happy to field any questions in the comments. Click here Prof. Saltzman’s article about this […]

  2. feldfrei Says:

    Thanks for the article – the combination of the theremin and its operation principle with the differential equations makes this show an educational “Gesamtkunstwerk” 🙂 The theremin (or termenvox) is fascinating (I would like to own one just to play – you know what http://www.youtube.com/watch?v=V0zQHNmz0gU 😉 and it was the pioneer of electronic instruments. The Beach Boys used a variant – the Electro-Theremin http://en.wikipedia.org/wiki/Electro-Theremin which is easier to play by means of a slider: http://www.youtube.com/watch?v=CelV7EbuV-A&feature=related
    Another similar instrument is the Ones Martenot http://en.wikipedia.org/wiki/Ondes_Martenot, which has a keyboard in addition to the slider. It was used e. g. in Olivier Messiaens “Turangalîla-Symphonie”: http://www.youtube.com/watch?v=wSZyV1Mh_eg
    Here’s an nice explanation (with a well-known tune at the end): http://www.youtube.com/watch?v=ybYIhomm5KM&feature=related

  3. Arturo Quirantes Says:

    Woh, the Geiger counter idea is cool! I want an app for that. Any chance the team will work it out for Android next time?

  4. Jennifer Gupta Says:

    I’m an astrophysics PhD student and on our latest astronomy podcast (the Jodcast) we were discussing the possibility of developing an app to use a cell phone to detect radio waves from meteors. Unfortunately it would probably drain the battery. Someone has been looking into cosmic ray detection using phones as well (http://www.distobs.org/)

    I’m not sure if David reads these comments but we were wondering if there was any chance you could get one of the characters to wear our podcast’s t-shirt if we sent you one. Email me 🙂

  5. discodave Says:

    Penny’s app was a much better idea. Instead of selling 70 licenses (for a million dollars apiece – Raj needs his submarine!), they’d sell several orders of magnitude more at a realistic price. Not only would they have the cool technical challenge of developing an algorithm comparing a real-world snapshot to the corresponding catalog picture, they’d impress a LOT of women in the process!

    • David Saltzberg Says:

      I read someone else’s blog post that started “BBT came up with a really cool app…” I expected to read that they were excited to write a differential equation recognizer/solver. Sadly, the next sentence was about the shoe app.

  6. Uncle Al Says:

    Léon Theremin went well beyond music,


    “The existence of the bug was accidentally discovered by a British radio operator who overheard American conversations on an open radio channel as the Russians were beaming radio waves at the ambassador’s office.”

    Heterodyne closure.

  7. mkjcaylor Says:

    ThinkGeek needs to stock a theramin, stat.

  8. Nik Says:

    A comparison between Sheldon and Lenin, that’s awesome.

  9. feldfrei Says:

    (OT): Congrats to the TBBT 3-year-renewal on CBS!

  10. Loc Says:

    The Big Bang rocks!! These guys can invent anything, I wish I was that smart.

  11. comradebazarov Says:

    This is a great blog professor (I am taking 1C right now)! I love reading your science explanations each week.

  12. ejarias@hotmail.com Says:

    Check this one !


    Respects to Mr.Paul Tanner !

    Cheers, Enrique

  13. S Halayka Says:

    Dear Dr. Saltzberg,

    TBBT show has a super huge Czech follower, and he knows quite a bit about physics too. I don’t know if you know who I’m talking about, but he’s ex-Harvard. I’ve even heard that the Czech might be part of the basis of the Sheldon character, but I don’t know if you as the science advisor is even allowed to know such things.

    The Czech is pretty nice underneath it all, and he does like to help people learn physics. Maybe if you know Jim Parsons, and you like the Czech and think he might be a real life Sheldon like the rumours say, then maybe you could please ask Mr. Parsons to say hi to the Czech. I know that this is a lot to ask of you and of Mr. Parsons, but I think it would make the Czech’s day very much! I dunno, I just thought it was a good idea to ask. I hope I am not being too offensive. 🙂

    Shawn Halayka

    P.S. TBBT is #1 in Canada for a reason!!! 🙂

  14. petrino Says:

    slight off topic, but a question non theless. is this…something? http://www.collectedcurios.com/SA_0674_small.jpg

  15. Bill Wickes Says:

    I’m at an intersection of interests for the “Bus Pants…” episode of TBBT: I’m a (retired) physicist and a fan of the show, and my daughter Lara is the musician who provided the theremin expertise for the production. I also built her first theremin. Readers here might be interested in reading her observations on the production, in an email she wrote for fellow thereminists just before the show aired: http://wickes3.home.comcast.net/~wickes3/BigBangExperience.htm. For a brief demo by Lara of the theremin, see http://www.youtube.com/watch?v=Plr6-Zwy-L4.


  16. Nathan Says:

    Hello, I have often tried to zoom in and see what are on Sheldon and Leonard’s book shelves and was hoping you might be able to name them and/or what you think would be on Sheldon’s reading list.

    • David Saltzberg Says:

      There are lots of real physics books. Not just throwaways, but real books that would cost over $100 to buy. Sorry there are too many to list. Keep hunting with your HD TV and let’s hope the characters don’t keep blocking the view.

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