Sometimes I can't seem to find just the right lab equipment I want for a particular experiment so I design it myself. Such was the case recently for a course I developed and teach entitled Science of Sound. This course is a natural science elective and deals with the physics of audio and acoustics. We start with a few very basic concepts such as harmonic motion. One of the laboratory experiments involves vibrating strings. I like this experiment because students can relate to it as most are at least familiar with guitars and other stringed instruments (the guitar players really like this one). I had some difficulty in designing a good experiment though. The basic idea is to verify the equation for the fundamental vibratory frequency:
where f is the fundamental frequency, l is the string length, T is the tension, and m-sub-l is the mass per unit length of the string.
Most of the lab devices I found were based on a vibrating box and used tuning forks to determine the frequency. Not really my cup of tea. For more flexibility, I designed the following and had the guys in our machine shop fabricate it:
It's pretty simple. The body is a solid piece of aluminum. At one end is a sliding fixture with an aperture for the string. At the other end is a fixed pulley. During the experiment, a wire or string (in this picture, a bass guitar string) is passed through the aperture and and over the pulley. The end piece is adjusted for a particular string length. Tension is added by hanging a hooked lab weight to the free end of the string (a nice reminder that tension is a force, and is found via f=ma where m is the mass of the lab weight and a is the acceleration due to gravity). The mass per unit length of the string is found by weighing the string on a lab scale and measuring its length. A small electro-magnetic pickup is placed near the string as the string is plucked. The pickup feeds a pre-amp which then feeds aTektronix TDS 3012 digital phosphor oscilloscope (DPO). (The DPO is located in the center of the top instrument shelf, between the function generator and DC power supply.) The DPO is a sampling o'scope with freeze frame, so the student just hits the acquire button once the initial transient attack is completed. They can then examine the waveform and determine its period, and thus, its frequency. The exercise is repeated for different masses, string lengths, and string thicknesses in order to verify the equation.
Although I could have used some off the shelf guitar pickups, these could get pricey for a multi-station lab. Instead, for about $15 I picked up some small cylindrical magnets and a pound of #30 magnet wire. I wound the wire around the magnets with the help of a variable speed drill, perhaps several hundred turns in a half dozen or so layers. This results in a usable signal, but not one as strong as a standard guitar pickup. In contrast, commercial units use around 5000 turns of #60 to #65 magnet wire. That's very small wire and it can be difficult to locate and is expensive, not to mention messy to deal with. Below is a pickup and components. In order to make them a little more robust, I plan on potting them in plastic after soldering on some #22 lead wire.
The results have been pretty good, and the unit is built like the proverbial brick outhouse.
Lovely! Reminds me of old woodcut illustrations of Pythagoras' experiments on strings.