2007 AAPT Summer Meeting
(Standing Waves, OHP)
Doug Johnson, Maria Salazar, Anatol Hoemke, Hector Maciel
California Polytechnic University, Pomona
3801 Temple Ave
Pomona, Ca 91768
This demonstration shows standing waves on a string. By varying the tension on the string, we can show the fundamental frequency, first harmonic, second harmonic, overtones, nodes and antinodes.
Construction of Apparatus:
3/4" Plywood, cut @ 11"x 20"
2x4 (Real dimensions 1.5"x 3.5"), cut as follows:
2 @ 9"x 1 5/8"x 1.5"
1 @ 6.5"x 3"x 1.5"
1 @ 3"x 1.5"x 1.5"
1 @ 3 3/16" round x 1.5" height
4 @ 1 3/4" flat head wood screws
2 @ 1 3/4" pan head wood screws
2 @ 1 1/2" pan head wood screws
6-12 @ 3/4" flat head wood screws
Cenco string vibrator
1" length 16 AWG wire
PVC 3"X3" Coupling hub
3 Corner brackets
Screen door tension roller (w/ screw)
2"x 1" Felt strip
18" length rubber string (from a paddle-ball toy)
Cable bracket (w/ nail)
Primer and spray paint (optional)
Approximate Building Materials Cost:
$10, not including the Cenco vibrator and paint
Soldering iron and solder
Sander and sandpaper
Jig saw (for the plywood piece center cut-out)
Power drill with various drill bits, phillips and flat-head driver bits, countersink bit
1. Make a small loop with the 16 AWG wire and solder it to the tip of the vibrating reed on the Cenco vibrator as shown. The holes already present are too small for the use of this project and can cut the rubber string we will attach to the end.
2. Cut the plywood and 2x4 to the required dimensions (as listed above). Mark the layout of the center cut-out as shown in the diagram and drill the corners with a 3/8" bit. Use the jig saw to cut the center out of the plywood piece.
3. Lay the plywood over the 9" blocks with them centered on the short sides of the plywood. Those are the legs that will act as a rail to keep the piece from sliding off the overhead projector. Clamp them in place firmly and drill two holes for each rail from the top face of the plywood into the rails for the 1 3/4" flat head wood screws. Countersink the holes with a countersink bit or a standard 3/8" bit. Screw the pieces together with the 1 3/4" flat head screws.
4. Place the other wooden pieces on the board in their designated positions as diagrammed. Mark all the exposed edges and corners of all the pieces, and sand them. If desired, paint all the pieces.
5. Center the Cenco vibrator on the top of the 6.5" block as shown and mark the two middle mounting holes with an awl. Drill them and attach the vibrator with the 1 1/2" pan head wood screws.
6. Drill two holes approximately centered and 1" apart completely through the 3 3/16" round wood piece from the top face. Attach the round piece to the plywood as diagrammed - the edge of the round wood piece should be about 1 1/8" away from the bottom and the side of the plywood, so that when the PVC piece fits over it the PVC is about 1" away from the bottom and side of the plywood. Place the felt strip against the inside of the PVC coupling and slide it over the round wood piece. The felt should give enough friction so that the PVC turns smoothly yet is somewhat tight.
7. Using the pliers, bend the screen door tension roller slightly at it's midpoint as shown. Using the screw included with the tension roller, attach the roller 1 1/2" out from the unsanded side of the 3"x 1.5"x 1.5" wood piece, as shown.
8. Using the masking tape, secure the blocks in position as diagrammed. Place the corner brackets in their positions as shown and mark the center of the screw holes with an awl. Remove the blocks and brackets and drill shallow pilot holes in all the marked spots. Using the 3/4" screws, attach the brackets to the blocks and the plywood base. Tie one end of the rubber string to the Cenco vibrator, and tape the other end to the PVC. Run the rubber string over the wheel on the tension roller and turn the PVC to increase/decrease tension.
9. Throw it on the overhead projector, plug it in, and see how many standing waves you can get!
Use of Apparatus:
Standing wave apparatus should be place on a overhead projector, so image can be displayed on white screen. Plug-in vibrator and adjust tension on string to harmonic of your preference.