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# The Physics of a ..... Glockenspiel?

Updated: Mar 25, 2021

In the last few days of 'normal' times last year, we hosted our annual Scifest event in the school. One of the many great projects was the one in the video opposite, where one of our 1st years had turned up with a home-made glockenspiel*. When the day was done I asked if it would be OK if I held on to it in the physics lab - as it would be great for looking at the physics of music and that it would tie in with Leaving Cert Physics too. I stored it on one of my window sills there, and the next thing I knew we were locked out of the school for nearly six months...

When I got back, the rubber bands had turned brittle (in itself some interesting physics) and the copper pipes had fallen off. I kept it in storage, intending to fix it up but not getting around to it until this mid-term (when - like most long-postponed jobs, it took about 10 minutes...)

Now that I have time to look at it in more detail, I don't have the student around to ask how he put it together. Hunting around, I found a few sites explaining how such a thing can be built. This one is pretty good.

I tapped the longest pipe a few times and ran the sound through the spectrum analysis app on my phone to figure out what frequency its at. The result is in the graph below, and looking at the lowest frequency peak in the upper graph (which is the one that corresponds to me hitting the pipe) I would estimate the frequency to be 1050 Hz - which roughly corresponds to C6 - two octaves above middle C on a piano.

The length of that pipe is 25 cm, and the wavelength in air that corresponds to 1050 Hz is about 33 cm. I had hoped that his might tie in with some of the maths we look at on vibrating strings or open pipes but it doesn't appear to do so. The thing is, I think it's the pipe that's vibrating and not the air inside, so its neither a string nor an open pipe. Looking down through the article I linked to above, it seems that the relationship between length and frequency is

L= sqroot(A/f) - where A is determined by the exact dimensions of the copper pipe used and in this case appears to be about 67 Hz m2. Once you have the value of A, you can determine what length all of the other pipes have to be create a key of C.

The frequency analysis also shows the presence of a rich mix of harmonics (as well as some rogue frequencies I can't explain).

The now-abandoned 2013 proposed syllabus included a requirement that students should build a simple musical instrument, and this would tick that box. All in all a pretty impressive project, I think. Particularly for a 1st year. And one that I might push on my TY students whenever we get back to normal times....

*I was going to call it a xylophone until the internet corrected me: I think the main difference is that a xylophone has wooden bars with metal resonance tubes underneath, and a glockenspiel just has metal bars....