A better description of resonance

This video is sponsored by The Great Courses Plus. A while ago I made a video, called a

better

description

of entropy, because I felt that the standard

description

of entropy wasn't very good, and I thought I could do

better

. It was a really fun video to make, so I thought it could become a series, and this is the next one, a better description of

resonance

. The standard description of

resonance

goes something like this. If you touch a glass of wine or pluck a guitar string, then the note you hear is the frequency at which that object likes to vibrate.

It is the favorite frequency of that object, it is the resonant frequency of that object and that is resonance. It's okay as a description, but I think I can do better. The best way I found to describe resonance is using this thing. It's called a Rubens tube. It is a hollow aluminum tube. At one end it's blocked with a piece of wood, at the other end it's blocked with a rubber membrane, and if I tap that membrane with my finger, it will send a pulse of pressure through the tube traveling at the speed of the sound.

When the pulse reaches this end, some of it is reflected and travels back through the tube to here, and then when the pulse reaches here, some of it is reflected and travels back in this direction. Then, when I hit the rubber membrane, a pulse of pressure bounces back and forth inside the tube, getting weaker and weaker until it finally fades away to nothing, but! What happens if I repeatedly hit the rubber membrane? So... I hit the rubber, the pulse goes through the tube, bounces back here. It comes back here, just when it gets to this side, I hit the membrane again and now the pulse is even bigger than before because I added something to it.

So now a larger pulse travels through the tube. Bounce and get here. Just as it gets here, I touch it for the third time and now the pulse is even higher again. And if I keep doing that, if I keep hitting the rubber membrane, at just the right moment, the pulse will get bigger and bigger. And that is resonance. Resonance is...getting the timing right, getting the frequency right, so that the energy you put into the system adds to the energy that's already there. That's resonance. So the frequency of the hits that I need... The one I need to get, that is the resonant frequency of the column of air inside this tube, but it is not the only resonant frequency of the column of air.

There are infinities. So, for example, if I hit the rubber membrane and a pulse comes into the tube and then I hit it a second time, now there are two pulses inside the tube that intersect like this, and then, the third hit occurs when the first touch comes back. Or you could hit the rubber membrane twice. So you know one goes in, another goes in there, maybe, and then a third goes in like that, and then the fourth touch doesn't happen until the first one comes back. But I'm still getting the timing right, so the energy I put in adds to the energy that's already there.

It's just that I waited a couple of taps to get in first. So what's that like when you have pulses coming from this direction and the reflected pulses come back and cross each other? Does it look like this. So the waves, coming from both directions, cross each other and add up, and when you add them up, you get something called a standing wave, where you have nodes and antinodes, the nodes are the points where there is no movement. and the antinodes are the points where there is a lot of movement. So how fast should I touch this membrane to see the effect?

Well, much faster than I can touch with my finger. It's actually an audible frequency, so instead of using my finger, I'll connect a speaker to the end, like this one. So if I can run the speaker, at the resonant frequency of this tube, then the energy I put into the system adds to the energy that is already there and we should hear that as an increase in the amplitude of the sound. We should hear the volume go up, so let's try that... Okay, so this is not one of the resonant frequencies of the tube, if I just turn up the frequency a little bit...

Okay... so the volume went up. I found the resonant frequency of this tube, the speaker is "hitting" the rubber membrane at just the right speed so that the next hit of the speaker encounters one of the pulses returning from this end and... we are adding to the energy that It is already in the system. That's resonance. The problem is that you can't really see what's happening because it's happening inside the tube and... the air is invisible. That's why Rubens' tube is designed to be set on fire. Before I set anything on fire, I actually changed the Rubens tube, the first one I showed you was one I built myself, and it was a while ago, and I didn't know what I was doing, and it's a little bit worse for wear . so I didn't feel comfortable setting that one on fire.

This is one I bought, the only problem with this one is that the speaker assembly is completely enclosed and I really wanted to show you the rubber membrane and the whole tapping thing. With this one, I feel comfortable setting it on fire. So we pumped butane through here and then set it on fire. The first thing you have to do is fill the tube with butane. You basically have to go above fifteen percent butane because it's a dangerous mixture. It's a stoichiometric relationship and it's explosive, so we just have to make sure that Mm. we get...

I can smell percentages. So. Hopefully, you can see the result of the standing wave in the flames. So these points are the nodes... here and here. These are the antinodes. So these points, the nodes (where the flames are small), are the points where the pressure does not vary much at that point. The high flames, those are the antinodes, those are the points where the pressure varies a lot, at that point, and let's see if we can find some higher ones. I checked some out there, let's see what we have. And that is the Rubens Tube. So what does all this have to do with the sound something makes when you hit it, pluck it, or run over it?

Well, any scenario like that you come across needs its own explanation. So let's look at a particular example. Let's take a look at wind instruments. So I have my wind instrument here, it's a bottle and I filled it with water and I can blow on the neck like this, *The bottle makes a nice note* And when I do that, I get a nice note. So why does this happen and how is it related to resonance? So when you make that noise with your mouth, that kind of *Whoosh* noise, that's white noise, and you may have heard white noise described as a mixture of all the frequencies within a range at the same time.

So when you hear that kind of hiss, hiss, sound, it's a whole range of frequencies mixed together. So when you blow on the neck of a bottle, you are pushing the air mass inward over a wide range of frequencies. But because of what we learned with the Rubens tube, only the resonant frequencies of the body of air inside it are actually amplified. So those are the ones you hear. Interestingly, when you listen to a wind instrument, you perceive the lowest resonant frequency, and all the other frequencies that are generated when you blow on the neck of a bottle like this simply increase the timbre of the sound, they do not change the perceived pitch of the sound.

So the quality changes, the timbre changes, depending on the balance of the resonant frequencies that are generated, and it is this balance that helps us distinguish one instrument from another. the case of plucking a guitar string is a little more k; actually, it's a guitar, I'm just huge. The case of plucking a guitar string is a little more complicated, it involves things like Fourier analysis and things like that. It's really interesting and I may cover it in a future video, but for now I'll leave you with the Rubens tube responding to the music. But before that, if you're interested in learning more about wave dynamics, resonance, sound and that kind of stuff, I can recommend an online course called physics and our universe and you can find it at thegreatcoursesplus.com. grateful to the great courses also for sponsoring this video.

If you want to see physics and our universe (the course, for free), you can sign up for a free trial at or click the link in the description. If you use that URL or the link in the description then they'll know I sent you which really helps me. The Great Courses Plus is an on-demand online video learning service, and if you sign up now, you'll have unlimited access to over 7,000 videos from top teachers and experts on the topics you love; In your case, probably. science and mathematics. *Playing on idle, by Kevin MacLeod* I hope you enjoyed this video.

If you did, don't forget to subscribe and click the notification bell. See you next time. Check out these other videos featuring resonance and the original video with a better description of entropy.