Gas station without pumps

2011 December 28

More on the slinky and the speed of sound

The Slinky Lab post got an interesting pingback from Engineering Failures » Secrets of the ‘Levitating’ Slinky, which describes the curious phenomenon that happens when you suspend a slinky vertically, then release the top end. The bottom end does not move for about 0.3 seconds, when the compression wave from the top reaches it. It might be worth videotaping that phenomenon in this week’s lab.

I think it might be interesting to try to calculate (either analytically, or as part of the VPython simulation) the movement of Slinky as you drop it. In particular, I’m curious at what point the compression wave becomes a shock wave (that is, when does the top of the slinky start moving faster than the speed of sound in the slinky). Note that the speed of sound in the slinky is best expressed as “coils per second” rather than m/s, in order to get a constant speed of sound in the non-uniformly stretched slinky.

The other lab/demo I was thinking of doing this week, measuring the speed of sound in a metal bar, is not going so well.  I was planning to use a setup similar to that in the Chapter 4 Lecture 3 video at http://courses.ncsu.edu/py581/common/podcasts/.  That is, a long metal bar, with a microphone at one end, tapped with metal striker at the other end.  A clock is started when the tap is made (a simple electrical connection), and the waveform is recorded at the other end.

The first problem was that I did not have a suitable microphone.  I found a quick workaround for that problem, as just last week my wife had given me a fine electromagnet that she had found in the street (we have a lot of “found objects” at our house).  The coil has a 68.3 Ω resistance and a laminated iron core, so waving a magnet around near the pole piece results in a fairly substantial electrical signal across the ends.  So I made my own “microphone” with the coil, a refrigerator magnet, and a folded piece of paper as a spring.  If I rest a piece of aluminum bar stock on it and tap the other end, I get a signal of about 0.3 v, which I can see clearly on my oscilloscope.  If it was a storage scope, I’d be almost done, since I could trigger on one channel and record on the other.  I might still have to do something like that with my analog scope.

What I had hoped to do was to use an Arduino to measure the time it took from the tap to the signal arriving at the other end. Using the micros() subroutine provides timing with a resolution of about 4 microseconds, and starting it on electrical connection from the tap is pretty easy.  I had initially thought to use the analogRead() function, but it is too slow: each analog-to-digital conversion takes about 100 microseconds, and the speed of sound in aluminum is about 6400 m/s, or about 150 μsec to go a meter.  I don’t think I can do speed measurements with that low a time resolution unless I had a bar of aluminum 100s of meters long.  That means that to use the Arduino for timing, I have to convert the analog signal to a digital one by some other means.  The most obvious method is to use a comparator chip, such as an LM339.  I looked through the spare chips I have from 30 years ago, and found one LM311-N14A chip, which has a comparator that takes only a +5v supply.  The data sheet even has a circuit for a “magnetic transducer”.  I tried the circuit, and found that  I needed to add capacitors across the input and the output to reduce noise that otherwise kept the comparator triggered.

Once I got the comparator circuit working, it was fairly trivial to hook everything up to the Arduino and write the following program:

void setup()
{
  //  put a 20k pullup resistor on pin 3
  pinMode(3,INPUT);
  digitalWrite(3, HIGH);
  //  put a 20k pullup resistor on pin 2
  pinMode(2,INPUT);
  digitalWrite(2, HIGH);

  Serial.begin(115200);
}

void loop()
{
  Serial.println("Ready");

  // wait for pin 2 to go low
  while (digitalRead(2)>0) {}
  long start_1=micros();
  while (digitalRead(3)>0){}
  long start_2=micros();
  Serial.print(F(" start_1="));
  Serial.print(start_1);
  Serial.print(F(" start_2="));
  Serial.print(start_2);
  Serial.print(F(" diff="));
  Serial.println(start_2-start_1);
  delay(100);

}

I tried it out with a piece of aluminum about 1.026m long, and got numbers in the range 272μsec to 304μsec, which would be speed of sound of 3380 m/s to 3780 m/s. That is a little slower than I expected. One possibility is that the comparator is not responding to the movement of the magnet toward the coil, but the rebound as it moves away. If I flip the magnet over, I get even longer times (784μsec to 884μsec), so I suspect the first orientation was the correct one, and the speed of sound in this aluminum alloy is a little lower than I expected, or the comparator circuit is adding some delays.

I’ll have to make a bit more robust way of holding the magnet and stuff, before Friday’s lab/demo, since everything is currently rather wobbly (the magnet is held to the coil with a PostIt note to act as the spring).

3 Comments »

  1. “just last week my wife had given me a fine electromagnet that she had found in the street”

    OK, I’m dying for more explanation of that one. Was the electromagnet by itself or part of some other object?

    I’m enjoying these posts about lab demos. I’d like to see you do a post about inquiry in science education and the “modeling physics” curriculum if you find yourself interested. My casual impression is that you are using a more traditional approach to teaching physics to your son — more guided instruction. I wonder if this is a deliberate choice, whether you think it generally more appropriate, more appropriate for your son?

    Comment by zb — 2011 December 28 @ 13:33 | Reply

    • My wife walks everywhere, and thus finds many interesting objects on the streets. Our house and garage are full of found objects (which may, someday, become part of an art project). The electromagnet had a broken plastic box with it, but she did not see any other scavengeable objects—I did not go to look at the remains. There are a couple of self-tapping screws through the laminated iron pole piece, which suggests that the pole piece was screwed into a piece of plastic. I have had a hard time envisioning any use for the particular shape for the pole pieces. It is not a complete magnetic circuit (like one would find in a transformer or audio choke), nor does it have a small gap (as one would expect in an electromagnet designed for lifting). The lamination of the core suggests to me that it was intended for AC rather than DC use. Perhaps I should take a picture of it and ask if anyone recognizes what it is from.

      I have read a number of posts praising the “modeling physics” approach, but I have not yet seen a clear description of what differentiates it from other approaches, so I’m not consciously following that method. I am following the Matter and Interactions book fairly closely, which the authors promote as

      Starting analyses from fundamental principles rather than from secondary formulas.
      Making macro-micro connections, based on the atomic nature of matter.
      Modeling physical systems: making idealizations, simplifying assumptions, estimates.
      Constructing computational models to predict the time evolution of system behavior.

      The pedagogic approach is pretty standard: I assign a chapter of the book with exercises. After we’ve all read a chapter, we discuss any conceptual problems the students are having, and compare results on the homework. If we don’t all three agree on the solution, we rework it together, trying to figure out what the mistake was (or difference in assumptions—some of the questions are open-ended enough to get very different results from different reasonable assumptions about missing information). If one of us has made a more serious mistake than a trivial arithmetic error, they are expected to redo the problem. We work on the labs together, trying to come up with a theoretical model of what should happen before we make the measurements, then trying to explain the measurements after the fact. I’ve not been insisting on lab writeups, and I feel guilty about that, since my son does need to work on his writing.

      I’m designing the labs myself, because we have different lab capabilities at home than most schools have. I don’t want to build anything expensive for a one-time class, so a lot of our labs are MacGyver constructions. I did just buy myself a hand-operated vacuum pump, so we could build a ping-pong ball cannon. At $36, I think that is the most expensive toy I’ve bought for the physics lab, though odds and ends often come to more (I spent about $20 today on steel rods, copper pipe, and wood dowels for measuring the speed of sound in various materials). The robotics club has been a more expensive educational investment ($300+ a year), but still an insignificant fraction of what private school would cost (I believe that the school he went to for 7th and 8th grade is now charging between $18,000 and $19,000 a year).

      Comment by gasstationwithoutpumps — 2011 December 28 @ 17:02 | Reply

  2. […] and stopped when the wave is detected at the other end.  As mentioned in my earlier post More on the slinky and the speed of sound, I used an electromagnet and a small refrigerator magnet to detect the sound wave.  The coil has […]

    Pingback by Speed of sound lab writeup « Gas station without pumps — 2012 January 3 @ 22:55 | Reply


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