### Notes:

The Case Studies: Waves Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Concept Builder can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

### Teaching Ideas and Suggestions:

A common thread in a Physics course is how does this quantity affect that quantity?  This Concept Builder focuses on these types of questions. There are three activities in the Concept Builder. The first activity - Wavelength and Amplitude - is designed to help students recognize wavelength and amplitude on a diagram of a wave pattern. They are given a wave diagram and then asked to identify from among a set of three other diagrams the one that has two times or one-half the wavelength and two times or one-half the amplitude.  The set of four Question Groups provide students with the skill and the confidence to make such decisions. It is a warm-up for the next activity.

The second activity - Frequency, Speed, and Wavelength - gets students thinking about how a change in frequency or speed affects the wave pattern. Two of the four Question Groups provide students with a wave pattern and then ask students to identify the wave pattern that results if the same medium (same speed) was vibrated with two times or one-half the frequency. Students must use the wave equation (v = f•W where W=wavelength) to think through how a change in frequency (at a constant speed) affects the wavelength. They will then need to use the Activity 1 skill in order to identify the wave pattern that exhibits that wavelength. The remaining two Question Groups provide students with a wave pattern and then ask students to identify the wave pattern that results if the rope through which the waves travel with twice or one-half the speed is shook at the same frequency. Students must once again use the wave equation (v = f•W where W=wavelength) to think through how a change in speed (at a constant frequency) affects the wavelength. They then identify the wave pattern that exhibits that wavelength.

The third activity - Tension, Density, and Speed - gets students thinking about how the tension or the linear density of a rope affects the speed at which waves move through the rope and the subsequent wave pattern. It is certainly the most difficult activity of the three activities in this Concept Builder. Two of the four Question Groups provide students with a wave pattern and then ask students to identify the wave pattern that results if the rope were vibrated at the same frequency but pulled to twice or one-half the tension. Students must first use the relationship between speed and tension and density to predict the affect of tension changes upon the speed. They then must use the wave equation (v = f•W where W=wavelength) to think through how a change in speed (at a constant frequency) affects the wavelength. They will then need to use the Activity 1 skill in order to identify they wave pattern that exhibits that wavelength. The remaining two Question Groups provide students with a wave pattern and then ask students to identify the wave pattern that results if the rope were vibrated at the same frequency but had twice or one-half the density. Students must first use the relationship between speed and tension and density to predict the affect of density changes upon the speed. They then must use the wave equation (v = f•W where W=wavelength) to think through how a change in speed (at a constant frequency) affects the wavelength. They then pick the wave pattern.

As you can see, the thrid activity is significantly more difficult than the first two. The speed-tension-density relationship is not a topic discussed in every Physics course and is often reserved for honors-level or college Physics courses. For those unfamiliar with the relationship, the speed of a wave in a rope is directly proportional to the square root of the tension to which it is pulled and inversely proportional to the square root of the rope's linear density. The linear density is defined as the mass per unit length of the rope. For instance, a thin rope (or string) may have a 50 gram/meter linear density but a thick rope may have a 500 gram/meter linear density. The relationship infers that waves travel fastest in tight ropes and slowest in loosely-helf ropes. And waves travel fasters in lighter ropes and slower in heavier ropes. When it comes to wave speed, "lighter and tighter makes for mightier." In fact four times the tightness leads to two times the speed. And four times the density leads to one-half the speed.

To gain a feel for the cognitive difficulty of this Concept Builder, we recommend that teachers attempt to complete one of the difficulty levels. Alternatively, the questions are provided in a separate file for preview purposes. In order to complete an activity, a student must correctly analyze each question for that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar question twice in order to successfully complete the activity. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through an activity, a system of stars and other indicators are used to indicate progress on the activity. A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the que of questions to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question in an activity has been analyzed, the student earns a Trophy which is displayed on the Main Menu. This system of stars and Trophies allows a teacher to easily check-off student progress or offer credit for completing assigned activities.

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.

### Related Resources

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Case Studies: Waves Concept Builder. These include:

• Minds On Physics Internet Modules:
The Minds On Physics Internet Modules include a collection of interactive questioning modules that help learners assess their understanding of physics concepts and solidify those understandings by answering questions that require higher-order thinking. Assignments WM1-WM4 of the Waves Motion module provides a great complement to this Concept Builder. It is best used in the middle to later stages of the learning cycle. Visit the Minds On Physics Internet Modules.

Users may find that the App version of Minds On Physics works best on their devices. The App Version can be found at the Minds On Physics the App section of our website. The Static Electricity module can be found on Part 5 of the six-part App series. Visit Minds On Physics the App.

Additional resources and ideas for incorporating this Case Studies: Waves Concept Builder into an instructional unit on Waves can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.