Waves and Resonance

[White ground with PHYGU! Logo and text: Standing Waves and Resonance]

[Cut to two men standing in a lecture theatre with a chalk board behind them.]

Orbax: Hello! I’m the Great Orbax and we’re here today with Dr. Mike Massa, and we’re going to discuss standing waves and resonance. 

Luckily for us Dr. Massa has a collection of oversized springs at home and he brought one in today. [Holds up a long spring that looks like a rope.] So we are going to put a wave into the spring. 

[Orbax and Massa each take an end of the spring, face each other and step backward until they are standing 5-6 meters apart.] 

[Close up on Orbax]

Orbax: I am going to generate a wave at this end and we’ll notice that it actually has an amplitude and it actually travels down to the other end. 

[Camera zooms out to show the wave moving along the length of the spring]

Orbax: And we notice that it does two things. One, when it hits the other side, it bounces back and two, that the two waves interfere with one another, and they create a kind of pattern. Now, you can actually put a wave in at a specific length [Move his end of the spring up and down to create a wave] that actually has a pattern that generate what we call a standing wave. Instructive and destructive interference are taking place and it occurs when you put in the length of a half wavelength. Increasing it again [Orbax moves his end of the spring faster to create faster waves] we can put in another half wavelength. Creating one full wavelength or two halves. Now, this is a mechanical wave. It’s a wave traveling inside of an actual object, [Orbax gets much louder] but something else that behaves like a wave, is something the we call sound waves! Sound!

[Transition to Massa and Orbax at the front of the classroom with some electronic equipment on the desk for a demonstration.]

Orbax: Sound is also a wave! [Turns to Massa.] Right?

Massa: Yeah. 

Orbax: And so you can actually generate sound with a speaker system like we have over here. In the same way that we established a standing wave with the spring with the mechanical wave, we can do the same thing with sound.

Massa: Sure, if we just change the wavelength of the frequency, you’ll hear it get louder just when we get to resonance. 

[Sound with changing frequency.]

Massa: You can hear as I change the wavelength up and down.

Orbax: That’s not increasing volume over there. That’s just by changing the frequency. 

Massa: Yeah.

Orbax: So the frequency comes up to resonance level it gets louder and then as you go past it, it actually gets quieter again, because you’ve put them in, in non-half wavelength intervals. Now, that’s the sound waves inside of here [Orbax gestures to the long tube set up on the table.] but you can’t actually see it. 

Massa: It’s the same thing as the mechanical wavelength we just saw.

[Video cuts to demonstration with the spring. And cuts back to the front of the lecture theatre.]

Massa: But, let’s take a look at it.

Orbax: So, what we’ve done here is taken this tube and we’ve filled it full of methane gas. Now, we’ve got small hole drilled into the top which gives us a resolution of effectively ¾ of an inch and if there is gas coming out of the sides then you can light it on fire. 

[Orbax uses a lighter and flames appear along the length of the tube at ¾ inch intervals.]

Orbax: This flame indicates there’s actually gas inside of this tube. Right? And right now there’s no sound. This gas I just coming out completely on its own we’ve got an even level of distribution. I would say the pressure is probably the same throughout this entire tube.

Massa: And what we’re going to do is, we’re going to send a standing wave through here and that’s going to alter the pressure at certain points. We’re going to get resonance where there are going to be parts where the pressure causes a large flame to come out and other regions where it inhibits the flame. 

Here I’m just going to turn the sound up a little bit, and you can see right in the middle we have a low amplitude of flame [Orbax puts his hand over the lower flames] 

Orbax: And it’s in half wavelength intervals right, we have a half wavelength here and a half wavelength here [Orbax gestures to each half wavelength along the tube.] And so you’ve got a whole wave. Constructive and destructive interference taking place just from the sound that’s being pumped into this tube full of gas.

Massa: If I tune this up just a little bit further [twisting knobs on the sound system.] You’ll be able to hear me get resonance again when the volume goes up.

[High pitch humming sound]

Orbax: There we go. 

Massa: I think that’s about where we are. 

[Flames get higher and three half wavelengths are visible.]

Orbax: So, this is three half wavelengths here.

Massa: There we go. 

Orbax: Same waves that we had with the spring, the mechanical way, no we’ve recreated that with sound waves inside of a tube. Just oscillating the pressure from high to low versions of pressure.

This is a one dimensional representation just exactly the same as we saw before with that spring before. 1D, straight line. Comes here, bounces pops right back at it. You can actually take this and adapt it to a 2D surface.

Massa: Okay, let’s take it there.

Orbax: Alright. You know what will fix this? More fire! Segue through the flames.

[Orbax turns up the gas and the flames get much higher.]

[Transition to Orbax, back at the desk with flames in front of him.]

Orbax: Before we were looking at a one-dimensional example where we watched a wave travel all along a spring, watched a wave travel through a tube, but we can actually also look at a more complex example in two dimensions. Here we’ve got a flame drum. Now instead of just a wave going from one end to the other it’s free to exist in this 2D environment.

[Cut to Orbax and Massa at the front of the lecture theatre with a round plate on the floor connected to the sound system with flames coming out of the drum. Massa is adjusting the frequency of the sound and the flames change shape with the change in sound.]

Orbax: And so you get the same thing right.

[Close up of drum with flames.]

Orbax: Resonance. You can hear the resonance.

Massa: Yeah. 

Orbax: Audibly. When you get a larger volume like this you’re in a resonance system now and you can see it now too. Again, visually you’ve got 2D resonance taking place. You’ve got big pressure, low pressure, high fire, low fire. 

[Orbax reaches for the gas valve.]

Massa: Okay, let’s move it up to higher frequency and see what else happens.

[A pattern of flames moves over the drum as the frequency is increased. It turns into an x shape or two lines crossing.]

Orbax: Oh there we go!

Massa: Okay. 

Orbax: Just keep bringing it up.

[Sound gets higher. The flame shape changes a bit to a thick x]

Massa: So now are we going to see three lines going?

[Flame pattern changes to look like a snowflake or three lines crossing.]

Orbax: There we go, it’s another visual interpretation of what resonance is. It’s a bit more complex than the simple one-dimensional example we saw before. There’s clearly more going on than just slapping and half-wavelength intervals, but its still resonance. You can hear it. As the sound goes up, it increases in pitch, you can see it now as well. And so we have the definition of resonance here with our flame drum.

And remember! Get back to work!

[Screen fades to a white with a circle around cut out of Orbax.]