I tend to be a rather practical person, if you can't give me an answer to "Where am I ever going to use this?", I'm probably going to look for something else to spend my time on. The activity I'm going to relate below, I did in my face-to-face Pre-Calc classroom when we were studying trig functions. I wasn't teaching physics at the time, although I think it would work very well in a face-to-face physics classroom.
I've always been interested in electricity and electronics, but when I was in high school I never had any money to spend on it (or anything else for that matter). I talked the local TV repair shop into giving me some junked TV chassis, and I took them apart using a soldering iron that was meant for doing plumbing work. That gave me a source for some wire, resistors, tubes, capacitors, etc. I could play around with those items.
After I started teaching, I happened to meet a person who did repair work for the local hi-fi store in town This was at a time when CB radios were in their prime. He was having trouble keeping up with the repairs and asked if I wanted some part time repair work. It sounded like a good idea to me, I saw it as a way to rationalize buying (and paying for) some of the electronic test equipment and hi-fi equipment I always lusted after.
During those years a local doctor in town who was into "green" in the late 70's, would bring in equipment to be repaired. I got to know him pretty well. One day be brought in a boom-box, that looked like it had been dropped from about ten feet, he indicated he wasn't asking that I repair it, but thought I might be interested in having it for parts. The door hung open on it, the front of the case was broken, the circuit board was cracked. I kept that boom-box in my garage for about a year, and then one day it occurred to me that my students might like to see and have an explanation of the inner workings of a boom-box, boom-boxes were in now and CBs were out.
I hauled my voltmeter and oscilloscope into school, along with the old boom-box. I had removed the screws holding the outer case in place. The students walked in and saw this in the front of the math classroom, the whole front side was hanging off of it. They weren't quite sure what to make of it. I had them come up around the desk, and then we did the following with this busted up boom-box:
1) I unplugged one of the speakers and then hooking the oscilloscope to the speaker, used the speaker as a microphone. I explained I could whistle a perfect C, and was probably the only person in Illinois that could do that. I whistled into the speaker and got a wonderful looking sine wave on the oscilloscope screen. They had been graphing the sine function in their math work, and mine looked just like their graphs, so they were convinced and nobody asked if the frequency was right. Of course several of them wanted to try it also, but with not having had any practice, their patterns would usually break up.
2) I then put in the audio cassette test tape I had, it had varying frequencies on it for testing frequency response. The tape would announce, "A 20 hz tone for checking frequency response" and that would be followed by the tone, the announcements and the tones would move up in frequency from the 20 hz to 20,000 hz. We watched the test tones on the oscilloscope and listened to them simultaneously. Math and science teacher know that as we move up through the frequency spectrum, the wavelength of the pattern on the scope gets smaller and smaller. Of course this corresponded nicely with f(x) = A sin (B x + C), where B is being increased.
3) Later came a section of the audio tape where they played a constant 330 hz tone for about a minute. This was for aligning the tape pickup head. I was able to use the steady tone, and adjust the volume so that students could see and hear the effect of changing A in the above equation.
4) On one side of the cassette head, there is a small screw that is used to align the tape head so that it is parallel to the direction of the travel of the tape. If the head is not parallel, the test tone from one channel will get picked up ahead of the matching test tone from the other channel, so on the scope you see the phase of the sine wave from one of the channels fall ahead of the phase for the other channel. By adjusting that screw, I could shift the phase over a range such that the right channel sine wave was ahead of the left, then to where they were the same, and then to where the left channel was ahead of the right channel. So now they were hearing and seeing the effect of C in the equation above.
I do believe the students left with a new perspective on the A, B, and C in the equation f(x) = A sin (B x + C), and why they might be of some practical value.
So far I have only talked about the cassette player in the boom-box. In the next blog posting I'll spend some time describing the AM, FM, and power supply sections of the radio that we were also able to look at and relate to the trigonometry we were studying.
Content related to this blog posting can be found at HippoCampus under Period & Frequency, Wavelength, and Sound Waves.