Weighted String: Building the Instrument

Transcription

1 Weighted String: Building the Instrument Overview The weighted string is a classic physics experiment, and has yielded some very important insights. Most classroom models use vibration generators and rope or cord, which makes a god visual demo but produces no sound. The demonstration model explained here works more like a monochord, and uses supplies that should be easy to find and relatively affordable wherever you are. It is also compact, relatively self- contained, and very adaptable to different needs and limitations This version requires some very basic carpentry skills and supplies. The lumber can likely be sourced from scrap, the tooling is minimal, and almost all of the hardware is cheap and easy to find. Everything that follows is hoped to be within the means of a busy educator working on a limited budget. Once you understand the basic configuration it should be easy to adapt the design to better serve your needs, and there are a few additional suggestions about doing that as well. Safety Concerns Because you will be using at least one power tool to put this together, it s important that you re able to safely navigate a wood shop and protect yourself while you work (including your eyes and ears). Additionally, since this model will be used in a classroom it s important to make sure that the wood and hardware present no splinters, sharp edges, or other hazards to students or to you. Finally, it s important to test the model fully before trying it in front of a class. Of particular importance is securing the non- weight end to your working surface. Materials Section of 2x4, roughly 4 long x Wood screws x 6 Metal square washer to fit screws x Upright mount pulley x 1* MSC #: Phosphor Bronze low E string x 1 (D Addario PB047, mm diameter, 9.030kg tension at concert pitch) 8 Zip ties x 4

2 Tools Chop saw or hand saw Drill press or hand drill 1.25mm jobber drill bit Sand paper, medium to fine grit T- square Wire cutters Safety glasses Ear plugs The upright- mount pulley is potentially the most expensive single item on the list, averaging around $10 per unit. If you want to limit expenses or can t find the right kind of pulley, a forged eye- bolt will probably work just make sure to get one fabricated as a continuous loop and not simply bent into shape with a visible join. If your string rests on such a join friction may fatigue the windings and cause the string to break, or the weight being used in the experiment might even force the string downward out of the bolt. Forged eye- bolts seem to be around the same price as upright- mount pulleys, but may be easier to find. If neither of those solutions meet your needs, reflecting on the mechanics of the experiment should make a workable solution evident to you. Strings The variety of strings available today makes it relatively easy to tailor the experiment to your needs and means. I m recommending a D Addario PB047 because it s extremely common, relatively cheap and its tension at pitch is nearly a round number. Additionally, D Addario sells many strings as singles so there s no need to throw away most of a set or re- calibrate the experiment for different gauges. Whatever you get, I recommend a wound string ideally a low E since they will generally be easier to anchor with our clamping arrangement. D Addario also provide thorough weight and tension information for every string they make. By all means shop around though; if you require an unusually thick gauge or extended scale length for example (both qualities that will enhance a strobe light display) Kalium Strings is likely your best bet. Construction You ll want to start with a fairly sturdy board; the string clamping mechanism needs to generate a lot of downward force, so you don t want the grain tearing ouit too easily. Find the centerline of your board and mark it. Mount the pulley exactly centered, as close as you can to one end. Mark the board at the center of the pulley s wheel. Measure 25.4 from this line and mark this is where you will clamp down the plain end of the string.

3 Cut two roughly 3 sections off of the end of the board. One will be drilled out to become your string block and the other will become the riser. You have some room to adjust the sizes here, depending on how much overhang you intend to leave for anchoring the un- weighted end. For the riser, position the block so that the edge nearest the weighted end is exactly at the marked scale length line. Drill and fasten the block, then extend your centerline marking over the top. Locate your screws and square washers. This washer is an unusual part; we re using it to make it easy to clamp the string without accidentally altering the scale length. To do this, align one of the flat edges of the washer with the edge of the riser block, then move it so that the centerline (and string) will just barely pass by the edge of the screw without having to bend around it. To make things really easy later make a large mark next to the side on which the string should pass. Mark the center of the washer and drill for your screw. When finished, affix the other washer and screw in the same manner to the end of the board directly behind the pulley. This will make stringing easier, and allow you to transport the apparatus more easily while it is strung. For the string block you ll need a 1.35mm diameter drill bit. For the sake of simplicity, it s probably better to make sure that the block (on the axis along which you ll be drilling) is at least a few mm shorter than the exposed length of the bit. Whichever axis you choose, find the center of that surface and drill your hole there. A drill press is the ideal tool for this but if you clamp the block in place and have a fairly steady hand the result should be fine. As pictured, you can follow up with a slightly larger bit to countersink the ball end of the string if you want to. Next you ll want to drill out the holes for your attachment system, whatever that is. My recommendation is to use zip ties because of their exceptional strength and affordability. The string listed here reaches concert pitch at exactly fifteen pounds, but other strings run as high as sixty. It may be wise to design for heavier weights in case you choose to try them later on. Pictured is a design with two holes. This is to allow the weight to pull the block straight down, which may be better for the string. With the zip ties in place, a strap or karabiner can attach the bag or container to the block. As long as you weigh your container and block in advance, the only real constraints are what you have on hand that will bear the weight. When it comes time to string, first eyeball your weight receptacle and see if your surface and floor will give the weight clearance to hang freely. If your anchoring mechanism is solid you might be able to let the weighted end overhand the edge of the surface though it s wise to be generous with the length of your plank if you intend to try this. If no nearby tables seem suitable, a pair of sawhorses or shop stands ought to do fine. The denser your weight the easier this will be. If you want to use water, the recommended string will take liters minus the weight of your

4 block and container. Photography suppliers also sell sandbags in pre- determined weights. When it comes time to string up, carefully unwrap your E string (the plain end is quite sharp) and thread it through your block making sure that the mounting holes are oriented toward the ball end. Pull the plain end of the string along the centerline of the board so that it passes by the square washer on the marked side. Check that your block is at a desirable height and then tighten the washer behind the pulley to hold the string in place while you wrap the plain end around its screw and lock down the other washer making sure that the flat edge is flush with the edge of the riser. Use your wire cutters to nip off the end of the string as close as you can get it to the washer. Frequency analysis It is likely that you will want to be able to measure the frequency of the vibrating string during your demonstration, especially before and after adding weight. The easiest way to do this is simply by comparison to a pitch pipe, tuning fork, or oscillator. If you want to measure the string s vibration in Hz however, you ll need additional equipment. Since our strings are ferromagnetic, one option is to use an electric guitar pickup. For maximum efficiency I recommend using a single coil model and orienting the coil parallel with the strings. One extremely cheap source of pickups can be found here. It also pays to ask a few electric guitar players if they have one they d be willing to donate to the cause; aftermarket pickups are extremely popular and the stock units they replace can often be found languishing in drawers. For this application the highest output single coil you can find will be ideal, but anything you can get will probably work. The leads of the pickup can be soldered directly to a mono jack like this one for plugging into a phone or other device with a 3.5mm jack, or this one if you want to plug into a guitar amp. In either case make sure you use MONO aka TS cables and adapters as opposed to STEREO/TRS. If you want the signal mainly for frequency analysis purposes it will likely work better to place the pickup centered about 6 from either end of the scale. If you wand to amplify the sound of the string and check frequency by ear, placement is less important. Either way, it s easy to experiment before committing. If the output is too low you can use shims to raise the pickup. Foam tape is a handy mounting adhesive, and can be layered to increase height if needed.

5 Troubleshooting For a wound E string at or below concert pitch, the anchoring system described should hold. If you find you need a more secure way of holding the plain end of the string I suggest looking to the conventional guitar tuning peg for inspiration or your actual solution. Mounting a tuning peg in such a way that it operates properly and preserves the correct scale length will take additional tooling and materials. For those with the required knowledge, multiple solutions will be obvious anything from using metal channel and L brackets to modifying a complete guitar. The instructions above are designed primarily to be simple and cheap to execute. If your ingenuity and resources inspire you to improve on the design, there s plenty of room to do so. One possible challenge is finding a set of weights that are compact enough to achieve full tension in the available space and, ideally, incremented in a way that facilitates the demonstration. The aforementioned photography weight bags seem ideally designed and relatively affordable. More compact but also more expensive are diving weights. Water is slightly cumbersome but cheap and easy to add incrementally and provides pretext for a slightly more topical physics lesson than the weight of lead by volume. Finally, getting the weight to hang free without overturning the instrument is a slight dilemma. My solution is to try and leave enough overhang at the opposite end that it s easy for a counterweight to get purchase. Still, lengthening the board can reduce portability and there are other potential options (C clamps, magnets, metal brackets, etc ). If you know what space you ll be using there may well be better solution possible. Hopefully there s enough here to equip you with a working demonstration model relatively quickly and easily.