Dr Hugh Hunt, Department of Engineering, University of Cambridge
Part of the show New Planets, Harmonics and the science of Sound.
Dave - Today we've got Hugh Hunt from the Engineering Department at Cambridge University in the studio and he's now holding a normal kitchen knife. What are you going to do with that?
Hugh - We've just heard from Ely about harmonics which you can get from this tube. Well actually if you listen around pretty much anywhere you can find harmonics all over the place. I've got an ordinary eating knife, not one of those dangerous ones you don't want to be holding by the blade, and if I tap it like this I can get a nice note. I'm holding it roughly half way along. But if I hold it somewhere else I can get a different note. So depending on where you hold it, you get different notes. If you hold it right at the end, you don't a note at all.
Kat - So that's holding it at the very tip of the blade.
Hugh - Yeah, holding it at either end you don't get any note at all. But it's quite interesting to explore where you have to hold a knife to get these notes.
Dave - I see you've got a big aluminium tube behind you. Is that a bigger version of the same thing?
Hugh - It is. As ever, it's always much easier to demonstrate these things cleanly if you have a contrived perfect experiment. So I've got a tube here that's six foot long.
Kat - It's like a scaffolding post isn't it?
Hugh - It is. It's hollow inside so you can play it like a digeridoo as well but I won't do that now. If I hold it at the end it just goes thwack. It doesn't do anything. But if I hold it in special places I can get really nice notes. I can get this one .
Kat - So you're holding it about half way up.
Hugh - There are lots of different places. I've marked this tube with different coloured strips so I know exactly where to hold it. Now this is getting the fifth harmonic, so it's starting from the very bottom and going up the harmonic series, a bit like that pipe we heard before with its harmonic series. If I hold it somewhere different, I can get the sixth one up, which is a bit higher. And I can get the seventh one holding it even higher. I can get the fourth one here.
Dave - So what's actually happening to the tube when you hit it?
Hugh - Well the tube is vibrating. If you imagine you've got a long piece of spaghetti, not cooked spaghetti, and you could bend it into the shape of a letter C. Well if you imagine that that piece of uncooked spaghetti was floating around in space, it could vibrate backwards and forwards like that letter C. If you used three fingers, you could bend it into the shape of a letter S and it would vibrate backwards and forwards in the shape of the letter S. You could go one step further and bend it into the shape of a squiggly letter or number three with another bit in it and you could make it really serpentine. It turns out that every time you introduce more bends, there's more energy in it and a higher frequency. That's the same with light. You might know that energy goes up with frequency.
Dave - So the pitch gets higher the more wiggles you have in the rod.
Hugh - That's right. So all I'm doing with these marks on the tube here is noticing that I can pick out these different harmonics.
Dave - So basically where you're holding the rod, the rod can't be wobbling.
Hugh - That's right. It's called the nodal point. And so the fifth harmonic on this rid has six nodal points and the sixth harmonic has seven nodal points and so on. If you draw a letter S then it has three spots that go through the metal and the C has got two spots.
Kat - So you can do that, for example, on a guitar. If you very gently put your finger against the middle of the string. Is that the same principle when you get a high pingy sound?
Hugh - That's exactly the same. When you're playing a stringed instrument such as a guitar, a cello or a violin, you can play the note and then just touch it in the middle and you'll get an octave higher. If you touch it a third of the way along, you get an octave and a half higher. This is all the harmonic series. The reason you heard The Last Post being played before in Kitchen Science is because it uses the harmonic series.
Dave - So what Wendy was doing with the tube was driving different harmonics at different times to make the tune.
Mandy - And Hugh, interestingly enough if you go into a guitar shop to buy a new guitar, the first thing you do is test the harmonics because that will tell you whether the bridge is true or not.
Hugh - Absolutely right. Harmonics are so wonderful that composers throughout the centuries have used them in all sorts of ways. There's a wonderful bit in Brahms' first symphony that just uses harmonics played on the horns. It's just magic.
Dave - Is this because it's hard to play anything but the harmonic series on a horn?
Hugh - Well yeah. If you want to tell your kid not to play any instrument, don't tell then to play the horn because they're the ones that get the blame when things go wrong in the concert.