Analyzing Musical Instruments
Williamsport High School
Washington County Public Schools
Students collected sounds from musical instruments as well as other sources using a CBL and TI-82 calculator or computers and interfacing devices. As the project progressed, TI-83 calculators were also used. Sound files were analyzed for fundamental frequencies and overtones.
The collaborative part of the project was two-fold. First, in order to have many signals to look at, all participating schools would "collect" as many instruments as they could. The results would be sent to Williamsport High School (WHS) or posted in web sites at the participating school with links on this web site. Secondly, it was hoped that students would participate in online discussions of their results. The online discussions ran into technical and scheduling difficulties and while at least 3 other schools besides WHS participated, only one school forwarded its data and posted it on its website. Those files are included below.
The project was initially designed as a culminating activity for a unit on waves and sound. Students would gain an understanding of the superposition of waves. As we switched between collecting devices, the project also began to encompass collection techniques and an understanding of how the sampling rate and number of data points could affect the analysis. So the project has great potential for teaching students about the nature of science.
The project also branched into a comparison between types of the same instrument (see the piano study) as well as a comparison between the tones produced by experienced musicians vs. novice musicians (see the note about the band instructor in the Second Attempt description below.) This project proved to have many teachable and potentially complicated aspects.
In the first phase, teachers will collaborate in the development of Web pages and their content as well as in the development of experimental ideas. During the first experimental phase teachers and students will work together to sample as many different instruments as possible as well as in the discussion of possible variations in experimental procedure and data analysis. Experienced teachers will assist less experienced teachers with the appropriate theory and techniques to carry out the experiments. The same collaboration will apply to the development of the Web pages. Within each building, collaboration between science and music teachers will be encouraged.
Students will use TI-Graph Link and CBLs to collect data or ULIs and computers, integrated software to clean up the files and Matlab to analyze and display the waves. In addition, Matlab will be used for tutorials in wave superposition and interference. One important aspect of this project is that it will highlight some limits of technology such as signal sampling and processing.
MSDE Core Learning Goals
Most notably, the same sound was not recorded by all three devices. Rather, the instrument was played for the TI-82, then the TI-83 and then the ULI. Thus, the cause for the differences in the appearance of the files could not be reliably determined. The ULI data showed the largest discrepancies compared to the TI-8x's. We considered our experimental procedure and data analysis carefully before using those again. In the next run, all recording devices will record the same session with the instrument - though they will all record different lengths.
After FFT analysis, students used the values in a Soundings program which was available from Canberra Grade School. With the possible exception of the trumpet, none of the data resulted in an electronic version of the instrument.
When the spring physics class got to sound, we not only wanted to eliminate some possible variables in the fall collection, but to try some other experiments. This time around, we only used the TI-82 and TI-83, but we used them simultaneously. So we know that the recordings are of the same note. Now we can draw some definite conclusions about the need for more data points and the accuracy of the FFT when there are only 99 data points. We recorded some new instruments and some we already have. Most notable is that the trumpet was played by the band instructor instead of a student.
While students were recording instruments and storing the signals on a laptop, other students were recording signals from and measuring the length of the chimes. Unfortunately, we could only use the TI-82 for this round, so signals are not sharp. Still some interesting results were obtained.
At a first glance, students can see that the instrument sounds are complex and consist of more than one frequency. They can also see that the FFT becomes sharper as more data points are collected.
For the Fall of '97, we tried again to use three measuring devices. Unfortunately, in the confusion, the teacher forgot to set the ULI-Sound program to collect more data points and so it collected the preset amount of about 250 points. Thus the TI-83 remains the instrument with the most sample points.
In this group, we managed to measure fewer instruments, but we did get two different students playing the trumpet. We now have 4 trumpet signals to compare.
In the Spring of '98, we successfully used three measuring devices. This time the ULI was set to collect 11100 data points. Judging however by the pictures, there may still be a problem with the MATLAB program when it comes to the ULI signals.
This time we gathered another flute, sax and violin signal to compare to the previous samples, as well as adding the tuba to our collection.