Notes

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:

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.

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

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.