The Name That Harmonic: Strings 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.

Many Physics courses will include a discussion of standing waves and standing wave patterns. Part of that discussion often includes an investigation of the mathematical patterns that can be found when comparing the various standing wave patterns that exist for a vibrating string. Two common mathematical patterns are:

- The frequency of the n
^{th}harmonic is n times larger than the frequency of the first harmonic. - The wavelength of the wave for the nth harmonic is given by the equation:
**W = (2/n)•L**where L is the length of the string.

This Concept Builder assesses students understanding of these two mathemaical patterns. There are three activities included in the Concept Builder. In the first activity - **ID the Pattern** - students must identify the standing wave patterns for the first six harmonics of a vibrating string. This is a *warm-up* and a pre-requisite for the next two activities. In the second activity - **Frequency** - students are given the fundamental frequency and the frequency of an unknown harmonic. They must identify the standing wave pattern for that harmonic. And in the third activity - **Wavelength** - students are given the length of a string and the wavelength of an unknown harmonic. They must identify the standing wave pattern for that harmonic.

This Concept Builder was intended as an in-class activity. We believe that it should be preceeded by some development of the mathematics of standing waves combined with some practice recognizing the relationships. Once students begin to understand the mathematics, use of this Concept Builder will be effective in helping them assess and perfect such understandings. The immediate feedback, repetitive practice, and built-in help assist students in internalizing these relationships.

In order to complete an activity, a student must correctly analyze each question in 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 level. 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.

This Concept Builder was intended as an in-class activity. We believe that it should be preceeded by some development of the mathematics of standing waves combined with some practice recognizing the relationships. Once students begin to understand the mathematics, use of this Concept Builder will be effective in helping them assess and perfect such understandings. The immediate feedback, repetitive practice, and built-in help assist students in internalizing these relationships.

In order to complete an activity, a student must correctly analyze each question in 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 level. 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.

There are several resources at The Physics Classroom website that serve as very complementary supports for the Name That Harmonic Concept Builder. These include:

- Reading:

Most students will find that Lesson 4 of the Vibration and Waves Chapter of the Tutorial is a perfect accompaniment to this Concept Builder. In particular, the following pages will be helpful:

Anatomy of a Wave

Harmonics and Patterns

Mathematics of Standing Waves

- 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 WM7, WM8, SM6, and SM7 of the Wave Motion module and the Sound and Music module provide great complements to this Concept Builder. They are 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 Wave Motion module can be found on Part 5 of the six-part App series. Visit Minds On Physics the App.

- The Calculator Pad: A collection of physics problems that are accompanied by answers and audio-guided solutions. Students and teachers will find numerous problems in both the Wave Motion and the Sound and Music Problem Sets that emphasize the need to analyze a harmonic pattern for a string.

View Wave Motion Problem Set

View Sound and Music Problem Set

- Curriculum/Practice: There is at least one Concept Development worksheet at the Curriculum Corner will be very useful in assisting students in cultivating their understanding, most notably ...

Mathematics of Standing Waves

Visit the Curriculum Corner - Wave Basics

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