AMASE: Resonance

[Guelph Physics Logo, electronic sound.]

[Cut to Mara sitting at the kitchen bar, with three different height and shaped wine glasses with water in them. She dips her finger in the water and runs her finger around the rim of the glass to make a resonant sound. Each glass makes a different sound.]

[Joanne enters.]

Joanne: Hey Mara!

Mara: Oh hi!

Joanne: Whatcha doin'?

Mara: Um, I was just playing with these glasses because dad taught me a trick last night when we were doing dishes. That if you get your finger wet.

Joanne: Okay, can I try too? Get your finger wet...

Mara: And then pick a glass.

Joanne: Okay, I'll do this one. 

Mara: Okay, I can do this one. 

Joanne: Kay.

Mara: Then you just rub it on the top. 

Joanne: Kay.

Mara: You gotta push a little bit 

Joanne: Yep. 

Mara: And um make sure your fingers are not touching the stem.

Joanne: The stem okay, so they're holding just the base down. Okay.

Mara: Yeah.

[Joanne and Mara both rub their fingers around the rim of a glass.]

[weird resonant noise]

Joanne: That is pretty cool! And do you notice something?

Mara: Yeah, the glasses make different noises...

Joanne: They do. The different glasses make different sounds. That's a phenomenon called resonance.

Mara: Phenomenon.

[Joanne laughing.]

Joanne: Yeah! A phenomenon! Called resonance. 

Mara: Okay.

Joanne: Okay.

Mara: And what do you do with this phenomenon?

[Joanne laughing.]

Joanne: Well, it applies to other things not just glasses. The idea is that objects like to vibrate or oscillate or shake at certain frequencies depending on their size and shape.

So, wine glasses, as you've seen, but also do you remember back in the summer when you were at the YMCA camp and they had that big long rope swing?

Mara: Oh yeah! That was fun!

Joanne: Super fun. So, it took quite a while to swing back and forth and back again on that big, long swing. It turns out that the frequency of the swing depends on the length. 

So, wanna do an experiment?

Mara: YEAH! 

Joanne: Alright... to the backyard!

[Cut to the backyard.]

[Music.]

[Two videos playing at the same time. Left side of screen: Mara is dressed in winter clothes, measuring the length of the rope on the swing with a tape measure. Right side of screen: Mara is dressed in summer clothes, standing on a platform and holding a rope. In both frames she starts to swing and a timer appears in the centre.]

[Cut back to Joanne and Mara at the kitchen bar.]

Joanne: Okay so when we play those two videos side by side, we can see that when Mara's on the big long swing it takes much longer to go one way and back again compared to the shorter swing, right.

So it turns out there's actually a formula that we can use to calculate the frequency of a swing depending on how long it is.

[Formula appears on screen:   \(\text{frequency} = \frac{1}{2 \pi} \frac{g}{\text{length}}\)   ]

Joanne: So you measured the length of the swing in the backyard how long was it?

Mara: About four feet.

Joanne: Four feet. We have to turn that into meters put it into our formula and that gives us a frequency of about half a cycle per second. Now we didn't measure the length of the rope swing at the YMCA camp because it was really, long and way high up in a tree, but we could estimate, right. So, how many times the height of your dad do you think that swing was?

Mara: Probably like two?

Joanne: Two? Okay so it was 2 Mara, dads long. That is not a standard unit of measure. 

[Joanne laughs.]

Joanne: We need to turn that into something... that we can use in the calculation. So, Mara's dad is about six feet tall, so that means about 12 feet long turn... that into meters put it into the formula we get a frequency of about 0.25 cycles per second.

[Frequency formula appears on screen:   \(\text{frequency} = \frac{1}{2 \pi} \frac{g}{\text{length}}\)   *Length in meters, not MaraDad units.]

Joanne: A quarter of a cycle per second. So, the shorter the length, the higher the frequency. 

Mara: Right. 

Joanne: And that corresponds to our experimental observations. Now, can you think of any other things where we change the length of a string say for example and it changes the sound?

Mara: Uhhh... ukulele?

Joanne: A ukulele! Absolutely! We do not have ukulele in the house but we do have a little guitar here.

[Joanne picks up a small yellow guitar.]

Joanne: So, the guitar has strings and the string is a certain length. If you want to pluck one of those strings which one you want to go with? The highest one? Okay.

[Guitar sound.]

Joanne: Okay so that has a certain frequency now if I press my finger down here halfway along or so then only this amount of the string can shake or vibrate... So, what do you think is going to happen now?

Mara: It's probably gonna get higher because, um the little glass made a higher frequency than the big glass?

Joanne: Right and the shorter swing had a higher frequency than the longer swing. Okay! Give it a go!

[Guitar sound.]

Joanne: Right! Much higher! Okay so the full length sounds like this...

[Lower guitar sound.]

Joanne: and half the length sounds like

[Higher guitar sound.]

Joanne: There you go! All right that is resonance. Objects of a certain size in a certain shape like to vibrate at a certain frequency.

Alright Mara you're gonna take us out here?

Mara: Oh yeah!

Joanne: With a rocking tune?

[Mara picks up guitar.]

Joanne: Thanks for watching Ask Me Anything Science Edition... take it away!

[Mara starts strumming and singing.]

Mara: science is fuuuuuuun sciiiience is fuuuuun. science is fuuuuuuun sciiiience is fuuuuun

Sorry, I'm bad at playing guitar.

Joanne: It was awesome. 

Thanks everyone. Send us your questions!