This apparatus is a low-cost wave-driver and amplifier driven by a free smartphone app for investigating wave propagation in strings. The wave driver can be used to examine properties of standing waves on strings as well as quantitative labs to investigate how string tension and string mass per unit length affect the wave speed. Not only does this set of labs establish the fundamental properties of mechanical waves, it provides an excellent experimental environment for students to collect and analyze data for a phenomenon that depends upon multiple variables.
Unfortunately, most science suppliers sell a wave driver apparatus in three parts: 1) the thing that does the shaking, 2) an amplifier, and 3) a function generator. Depending on the supplier, one full setup costs between $500 and $1000. This version costs about $30 in parts and takes advantage of the capabilities of your smartphone.
Design Features:
The apparatus consists of a 4-inch speaker, a 50 Watt mono amplifier circuit, a 12-volt power supply, and some laser cut acrylic pieces that tie things together. All parts are mounted to a central acrylic plate that includes notches for cable management when not in use. If you don't have a laser cutter, the base could be cut from wood. The device slips over a ring stand with a flat metal base. The metal rod acts as one anchor for the string and the acrylic pyramid mounted to the speaker cone shakes the string. The magnet in the base of the speaker sticks nicely to the metal base, and a hole in the acrylic plate locks it onto the ring stand rod. This makes the apparatus much heavier so that it doesn't wander across the lab table.
Parts:
4-inch speaker, 4 ohms. You want a single speaker cone, not the full range type that have small cones for higher frequencies nested inside. Also, a large diameter magnet on the speaker base is better for this apparatus.
~50 Watt mono amplifier circuit. On eBay, I like "DC 12V-24V TPA3118 BTL 60W Mono Digital Audio Power Amplifier Board Amp Module".
12-volt DC power supply, the wall-wart type. On eBay, I like "12V 2A 24W Power Supply AC 110-240V To DC". These are commonly used to power LED light strips and are easy to find.
Mono audio cable with 1/8" jacks at both ends. Cut the cord in the middle, and you have cords for two setups. The cord delivers the signal from the phone to the amplifier.
Low voltage wire
1/8" wood or 1/8" acrylic base 8" x 4.8".
1/16" plexiglas for the attachment to the speaker cone or a styrofoam cup.
String and shock cord of various thicknesses.
4 bolts 1" x 1/8" with nuts to attach the speaker to the base.
4 #4-40 x 3/8" bolts and nuts to attach the amplifier to the base.
Software:
There are a variety of smartphone apps that feature tone generators or frequency generators for free. I've been using one called "Function Generator" on an iPhone which works fine, though it's filled with pop-up ads. You want a program that allows you to increase or decrease the frequency by tapping to increase or decrease the frequency in 1 Hz or 10 Hz increments. Interfaces that use a slider or require you to type in the frequency are difficult to use for this application. I want to give a shout out to the Physics Toolbox app that gives you access to all of the sensors in your phone. (Check it out!) The Physics Toolbox has a tone generator for Android that allows you to change frequency by tapping, but it does not work that way on iOS. Also, because newer iPhones no longer have a headphone jack, an adapter is needed.
Tools:
A laser cutter is nice, but not necessary to cut the base. If working with a saw and drill, I would suggest cutting the base from 1/8" masonite (tempered hardboard).
Soldering pen and solder
Hot glue gun and hot glue
Wire cutter/stripper
Screwdrivers
Assembly:
Cut the base plate according to the template.
wave driver base (.svg file)
speaker attachment (.svg file)
Start the wiring by clipping the plug off of the power supply. Strip and tin the ends of the wire. Solder the red wire to the power + terminal on the amplifier board, and the black wire to the power -.
Strip and tin the wires from the 1/8" audio jack and solder them to the input terminals.
Cut two wires about 6" long, and solder them between the out terminals on the board and the terminals on the speaker.
Test to see if the connections work by plugging in the power and plugging the audio jack into the phone. Play some tunes!
The speakers I purchased had a fabric covering protecting the speaker cone. I cut off the fabric careful not to damage the speaker cone. Because I have access to a laser cutter, I cut the speaker cone attachment from 1/16" acrylic, but a styrofoam cup could also be used. A few dabs of hot glue attach the speaker to the cone attachment. The vibrating string rides in the groove in the plexiglas. Gently denting the rim of the base of a styrofoam cup will form a groove to keep the string in place.
Use the nuts and bolts to attach the speaker and the amplifier board to the base plate.
Use hot melt glue to attach the wires to the base plate. This acts as a strain relief so that a tug on the wires doesn't disconnect them from the amplifier.
Use dabs of hot melt glue to affix the speaker attachment to the speaker.
Tie loops at the end of each of the strings. I like using a figure-eight bight. Adjust the position of the string on the ring stand so that it exerts a light downward force on the speaker attachment.
Elastic shock cord produces particularly well-defined nodes and antinodes. Because it noticeably stretches as the tension increases, the mass per unit length of the cord changes. Therefore, use the shock cord for demonstrations and use the various thicknesses of cotton and nylon string for data collection. In the photos, I just let the cord dangle over the edge of the table where it is attached to a hooked mass. Especially for the quantitative measurements, bend the cord over a pulley to help ensure a consistent tension throughout the cord.
If the ring stand is clamped down, the tension can be made quite high, with several kilograms of mass hanging from the far end of the string.
Teaching ideas:
Use a long slinky to develop the ideas of pulse propagation and resonance first. Working in pairs, students can find the resonant frequencies and determine the corresponding wavelengths. From this investigation, students find that wavelength is inversely related to the frequency. The proportionality constant is the wave speed.
Use an elastic shock cord to demonstrate resonance with the apparatus. Tune the input frequency until a standing wave appears and ask students to predict what other frequencies will make a standing wave appear. Also point out that even when the volume is low, at the resonant frequency the amplitude of the antinodes is large.
In a darkened room, illuminate the vibrating string with an adjustable-rate strobe light. The strobe frequency can be tuned to "freeze" the wave in place, make the wave appear to move in slow motion, and make it look like there are two or more vibrating strings.
From the initial investigation, students see that, while wavelength and frequency affect each other, they do not affect the wave speed. Ask the students to brainstorm the variables that might affect the wave speed. Likely ideas are tension, string thickness and stiffness, among others. It will take some discussion to develop the concept of the linear density of the string. Ask the students to design an experiment to determine how these variables affect the wave speed. They should recognize that two experiments need to be conducted: wave speed vs. tension while keeping the linear density constant, and wave speed vs. linear density while keeping the tension constant.
Graphing wave speed vs. tension while keeping the linear density constant results in a side-opening parabola. Students can linearize the graph by plotting wave speed squared vs. tension. A careful analysis of the slope value and units shows that it is the reciprocal of the linear density of the string. If every lab group uses a string with a different linear density, performing this experiment may be enough to determine the pattern.
Graphing wave speed vs. linear density while keeping the tension constant yields an inverse relationship. (Note that it is challenging to get enough strings of different linear densities of strings to show a clear relationship.) Attempting to linearize the graph by plotting wave speed vs. the reciprocal of the linear density produces a side-opening parabola. A second linearization attempt, plotting wave speed squared vs. the reciprocal of the linear density, produces a linear relationship where the slope is equal to the constant tension.
This apparatus was offered as part of a make-and-take workshop hosted by STEMteachersNYC, last run in 2017. Sign up for STEMteacherNYC's Google group to learn about future offerings of this workshop.
Originally posted on my previous website January 20, 2017.
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