Most physics teachers will have to demonstrate standing waves at some point in the school year and there are a number of standard demonstrations which can be done with school lab equipment. When teaching about them, I also show videos of standing waves I can’t recreate in the classroom and the one above is a lovely addition to my resources for this topic. This video also reminded me of a piece of art I saw at the Tate Modern several years ago – Kinetic Construction (Standing Wave) – which was the first time I saw a Physics demonstration presented as “art”.
As Pendulum Week continues here you’ll have noticed a pattern building up: that pendulums crop up in all sorts of demonstrations, but it’s often rather tricky to pin down satisfying explanations for their behaviour. Pendulums appear simple and straightforward to grasp, which is usually a good sign for demonstration tools as we want audiences to engage with ideas or behaviour and not be distracted by unfamiliar apparatus. However, I wonder if it’s possible that pendulums are too simple, in that their apparent simplicity seems to lull us into forgetting their subtleties.
Heck, unless you’re in that sin θ ≈ θ small-amplitude space you haven’t even, technically, got simple harmonic motion. Most of the time, pendulums don’t even swing like, well, pendulums. Ouch.
It feels like it ought to be possible to link pendulum demonstrations together in a neat story. A mass on the end of a string is about as simple as physics apparatus gets, surely there’s a delightful sequence of demos which can build successively, one on the other, to arrive at something complex and surprising and revealing about the world? That’s got to be possible, right?
Perhaps it is, but the origin of this series of posts lay in my noticing that pendulum demos aren’t alike, and the distinctions seem to me to be of the subtle-and-confusing kind rather than the subtle-but-illuminating kind.
Probably the best attempt I’ve seen to navigate the resulting swamp was by my colleague Marty Jopson, who made this film for the first series of Science Shack (skip to 2:40 for the start of the show):
Marty and I were co-producers on the series, and if I remember correctly he won awards for this show. I wasn’t, I should say, much involved with this episode (harrumph), but it’s still worth a watch. It gets into some of the subtleties about resonance and synchronisation that we’ve seen in this series of posts.
Pendulum Week heats up with… coupled pendulums:
(First embed, doubtless of many to come, from the prolific Brady Haran at Nottingham.)
Look in any of those interminable/popular[delete as applicable] ‘Exciting Fun Science Things to Do on a Rainy Day! Science!‘ books and you’ll likely find this old standby, more commonly done with potatoes rather than creme eggs.
It’s not one of my favourites, partly because I think it needs careful performance to appear as amazing as is usually claimed, but also because the subtlety of explanation required hardly seems worth the effort. This film, for example, doesn’t tell us very much. The explanation bit goes:
“There are little forces as [the connecting string] goes out of line that pull from one to the other, transferring energy from [the first pendulum] … over to that one, and then back again.”
Hmm. All that’s doing is describing what we see and replacing the word ‘swing’ with ‘energy,’ and I’m not a big fan of using ‘energy’ as an arm-wave explanation. Robert Winston’s book, snarkily linked above, explains pendulum movement in terms of gravity and momentum, then adds:
“If two pendulums are attached to the same piece of string, they pass their motion back and forth between each other. One pendulum swings, pulling the string it’s hanging from to and fro. This transfers energy to the second pendulum, which starts swinging itself.”
…which, again, is a reasonable description. Is it an explanation, though? I’m unconvinced.
Neither of these ‘explanations’ has begun to cover why it matters that the pendulums are the same length, let alone pesky details like: the demo still works if the connecting string is perfectly taut, when the driving force is delivered by torsion at the suspension point rather than lateral displacement.
But when you try to write a more satisfying explanation you end up in a bit of a mess. I know I did when I wrote this demo into a children’s TV series back in about 1998. A satisfactory explanation has to include (or at least skirt around) energy exchange, mechanical impedance, and resonant frequency – the sheer amount of physics required is, to my mind, beyond what the demo itself will support.
Better, I think, is this variation:
…which is much more clearly about resonance. The inverted spring pendulums also break the visual connection with the phase demonstration in the previous post in this series, which I think would reduce the risk of confusion were one to attempt linking several of these demos together.