Published on May 15, 2014
Everyone enjoys listening to music—the universal language in which a variety of sound frequencies combine to excite our sense of sound. Now these sounds can also excite our sense of vision!
Have you ever heard what happens when two audio tones of slightly different frequencies are played simultaneously? The result is a rhythmic pulsing of the sound--a phenomenon called beats in the world of physics.
In this lesson, your students will hear and see beats using the littleBits modules from the Synth Kit and the Arduino module. In addition, students will discover the differences between "square" and "saw" waveforms, and understand why "the 'square' waveform has a rich, powerful character and the 'saw' waveform has a more mellow, rounder character." (Quote from the littleBits Synth Kit Guide)
Students will be able to:
Use littleBits to see and hear beats, waveforms of pairs of slightly different frequencies
Define wave interference and explain the difference between constructive and destructive interference
At the conclusion of the lesson, assess student understanding by asking them to explain beats using what they learned about wave interference.
NGSS Disciplinary Core Ideas
PS4: Waves and their applications in technologies for information transfer
NGSS Science and Engineering Practices
SEP3. Planning and carrying out investigations
Duration: 1 45-minute class
It is suggested that students begin by having both oscillators set to saw waveforms. (Students can repeat the procedure later with square waveforms.) Have students set both oscillators at tones similar to those of middle C on the piano and then adjust the controls until they have the two oscillators producing the rhythmic pulsing common to beats. The two oscillators will be very close together in frequency. Students will need to adjust the controls so that they are hearing from, say, three to seven beats per second. (Very high tones (high C or higher) will produce charts that are a bit crowded, so middle C or lower is best.)
Note that the Arduino module's micro-USB cable must be connected to a computer, and the computer must have the Arduino IDE software installed. It is important to remind students that THE ARDUINO SWITCHES SHOULD BOTH BE SET TO ANALOG.
Depending on how familiar students are with using the Arduino module, it may be helpful to model setting-up the Arduino module ahead of time.
When ready, have students power up the Arduino module and start the Arduino IDE software. They should select Tools>Board>Arduino Leonardo. Then students select Tools>Serial Port and select the serial port that the Arduino will use for communication. The name of the port will depend on the computer’s operating system. On a Mac, it will start with /dev/tty.usbmodem... and a PC will start with COMM… In Windows, you can look for the USB serial device in the ports section of the Windows Device Manager. If you are on a Linux machine, the port will look like /dev/ttyUSB…
Instruct students to open the sketch file called Beats.ino and upload the sketch to the Arduino module. Students will see the yellow rx/tx LEDs blink on the Arduino module while the sketch is uploaded. After the blinking stops, students will then have 15 seconds to start the serial monitor by selecting Tools>Serial Monitor from the IDE. After the 15 seconds have elapsed, data collection will automatically begin and results will appear in the Serial Monitor.
The Arduino Sketch (program) on the Arduino module has collected numerous data on sound level for each oscillator and the combined sound from both oscillators for a period of only one second. The serial monitor should appear similar to that shown in the figure above.
When students are done collecting data, they can transfer the data from the serial monitor to Excel. Again, consider walking your students through how to complete this step before asking them to do it on their own. First, students need to uncheck “Autoscroll” in the bottom left corner of the serial monitor and then use the mouse to drag and select all of the data beginning with the data line containing the column headers "Time Osc1 Osc2 Combined". Then, they should open the attached Excel .xlsx file called Beats Template.xlsx, right-click on cell A1 and select Paste.
Students should see the data in the Excel workbook on the far left. In addition they will see two charts. The top chart shows the waveform of the sound waves from the individual oscillators for only the first 0.1 seconds of data collection. The bottom chart shows the waveform of the combined sound waves, which is what you hear from the synth speaker. This chart shows a full second of data collection.
A portion of what the charts may look like is shown in the image above. Students should see saw waveforms for the separate oscillators, and a beats waveform for the combined oscillators.
A cycle is the time from peak-to-peak for either saw or square waveforms. Determine the frequency of each of the individual waves from the top chart in cycles per second (cps). In physics, a cycle per second is known as a Hertz, or Hz for short.
Have students follow these steps to determine the frequency:
1. Measure the time for as many full cycles as possible by noting the start time for the first cycle's peak and noting the end time for the last cycle's peak, then finding the difference (call this D) in start and end times. Do this for both the oscillator waveforms.
2. Divide the above time (D) by the number of cycles counted. This gives the time between each cycle (call this T). In physics, the time for one cycle is known as the period of the waveform.
3. The reciprocal (1/T) gives the frequency (call this f) of the waveform in cps (or Hz).
Now ask students to find the difference in the frequencies of the two waveforms. Physics tells us that this difference should equal the number of beats that we hear per second.
Discuss the following questions with students:
-How many beats do students see on the bottom chart, which gives exactly one second of the combined waveforms?
-Is the number of beats that students see pretty close to what they calculated based upon knowing the frequencies of the two separate waves?
-What are possible sources of error in this experiment?
Students can now repeat the experiment but change the oscillator switches so that they produce square waveforms. They will notice that the square waves tend to be either LOW or HIGH with quick jumps between LOWs and HIGHs. The resultant beats are also either LOW or HIGH, with distinct boundaries. Discuss the differences students observe between the saw and square waveforms.
Study the saw waveform graphs in some detail.
Looking at the top chart of the two individual saw waveforms, students will notice that, at times, the waves are in sync with each other, with peaks meeting peaks and valleys meeting valleys. At these times, the waves interfere with each other constructively. At other times, they are 180 degrees out-of-step with one another, with peaks of one waveform close to meeting valleys of the other waveform. At these times, the waves interfere with each other destructively.
With students, note a time of constructive interference, and then look at that time in the bottom chart of beats. Is the beat at that time at its loudest or at its softest volume?
Note a time of destructive interference, and then look at that time on the bottom chart of beats. Is the beat at that time at its loudest or at its softest volume?
At this point, students should now be able to understand and explain the following statement in the littleBits Synth Kit Guide:
"The 'square' waveform has a rich, powerful character and the 'saw' waveform has a more mellow, rounder character."
To assess student learning, consider asking students to complete an exit ticket asking for a complete explanation of what causes beats from basic physics principles of wave interference.