# Resonance

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## Objective

Students apply the definition of resonance to a variety of real-life examples.

#### Big Idea

Resonance is a vibration of large amplitude in a mechanical system caused by a small periodic stimulus of the same frequency as the natural frequency of the system.

## Context and Supplies

Today students learn about the concept of resonance and how it is applied to several situations. There is a mix of demonstrations, videos as well as reading and writing to expose students to several ideas about resonance. Students apply the wave equation which they learn in Wave Hello. Interference (Slinky Rules) and standing waves (Standing Waves) are also important concepts in resonance. Due to standardized testing, the school has an early dismissal today and the class period is only 25 minutes long.

The supplies needed for today's activity include a rod with three stoppers tied to it with string, with each string a different length. In addition, internet access and a projector are needed to play some YouTube videos.

NGSS Science Practice 6: Constructing explanations (for science) and designing solutions (for engineering) and ﻿CCSS Math Practice 3: Construct viable arguments and critique the reasoning of others are applied as students provide examples of resonance, defining the parts of the system that vibrate and the small periodic stimulus causing the system to vibrate. The NGSS performance standard this topic applies to is HS-PS4-1: Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.

## Resonance Video and Definition

10 minutes

As class begins, I have the definition of a standing wave that is on my Resonance Powerpoint on the board to review what was learned in Standing Waves. This reminder of standing waves, nodes and anti-nodes is essential as I show the students a video on the Shattering Wine Glass. This video is from the Discovery Channel show, Time Warp and it shows a crystal drinking goblet shatter from sounds waves in slow motion. I show this video at the start of class because it is the perfect primer to discuss resonance.

After the video, I display the definition of resonance. The definition is "Resonance: a vibration of large amplitude in an object or system caused by a small periodic stimulus of the same or nearly the same frequency as the natural frequency of the system."

After they write this definition down, I have them do a turn and talk for 60 seconds. I list the important terms from the resonance definition and students are to identify those items in the video. The terms from the definition are listed below with the connections to the video in bold.

1. Object experiencing large amplitude: the crystal
2. Small periodic stimulus: the sound waves
3. Natural Frequency: 337 Hz

I then call on random students to supply the object from the video that connects to the definition term. I also ask them to justify their response. It is important that students be able to apply this definition to real-life examples, otherwise it is not very meaningful. At this time, I assign homework where I ask students to provide two more examples of resonance. They can use any references they like and they are to submit those examples to me via email with their examples connected to the three parts of the definition listed above.

## Tacoma Narrows Collapse

10 minutes

I show one of the many YouTube videos about the Tacoma Narrows bridge collapse. This engineering disaster is a staple of high school physics instruction and is a must show when teaching about resonance. I play the video to show how standing waves formed on this bridge, students are free to ask questions, but they are primarily observers.

While the video plays, I pause it to point out how the bridge oscillates so that we see nodes and anti-nodes form. I also point out that the sides of the bridge are 12 feet tall which means that the areas where the anti-nodes have formed move up and down over 30 feet in just a few seconds. The motion as this spot is as extreme as any amusement park ride they can go on!

Unfortunately, resonance is not the explanation for the collapse, at least not entirely. The explanations on the internet for why the Tacoma Narrows Bridge collapsed are varied. Some claim resonance, others vortex shedding and others, such as Mintute Physics, claim that aeroelasticity was the primary cause. Whatever the cause, it is clear that a standing wave formed along the length of the bridge and the amplitude of the standing wave was too great for the structure to handle.

## Closure: Resonance Challenge

5 minutes

To wrap up class, I hold up a small rod that has three stoppers tied to it with different length strings. I issue a challenge: whoever can get the three stoppers to swing back and forth with the same frequency receives extra credit. Because the stoppers are pendulums of different length challenge is impossible to perform UNLESS a student is clever enough to wrap the stoppers around the rod until they are the same length, which is what happens in the solution found video.

I then explain that the rod with matching length strings is like a crystal wine goblet that resonates with sound waves. The stoppers at matching lengths vibrate at the same frequency the same way the molecules in a crystal goblet vibrate as the same frequency because of their regular repeating structure. When the length of the strings are of different lengths, no one can get the stoppers to swing at the same frequency. This is like the molecules in a drinking glass. They are irregular, not uniform, and so do not have a single natural frequency.