Sound Beats and Sine Waves
Jernita Randolph Tech Review
This applet allows students to listen to and see interference patterns produced by sound waves with similar frequencies. Students can test their ability to distinguish and match sounds like musicians and sound engineers. They can then calculate the number of "sound beats" they will hear based on the frequency of each sound. There are learning materials for the applet which include a vocabulary sheet and an exploration guide to help students navigate through the activity.
Students have the option of listening to the sounds and/or getting a visual representation of the graphs. If students are working on the activity individually or in small groups, I would highly recommend the use of headphones to decrease the amount of noise and distractions. The image below shows what the Gizmo looks like when nothing has been selected.
Sound Beats and Sine Waves Activities
![Picture](/uploads/3/1/6/0/31605851/461655.jpg?609)
The student exploration guide is comprised of 4 activities, a warm up, Activity A, Activity B, and Activity C. There are also 2 questions which should be discussed or reflected on prior to the activities.
Warm Up
The warm up activity guides students through the basics of how to use the Gizmo and asks them to make an observation about Sound A and Sound B.
Activity A
The question being addressed in this activity is: "How do two waves with the same frequency interact?"
The activity introduces some new vocabulary and guides students through the process of exploring sound waves with the same frequency. After they have had an opportunity to work through the activity they are then asked to "draw a conclusion" about what they have observed.
Activity B
The question being addressed in this activity is: "How do two waves with different frequencies interact?"
In this activity students actually have to collect data, create a table and then make a prediction using that data. It discusses constructive and destructive interference and how they affect sound. This activity builds on the vocabulary and concepts introduced in Activity A.
Activity C
The question being addressed in this activity is: "How do the number of beats relate to the frequencies of the two sound waves?"
Students once again have to collect data and also calculate the number of beats per second by interpreting intervals on the frequency graph. The data is collected in a table format. They will then use this information to analyze the relationship between the frequency and the number of beats per second.
Students once again have to collect data and also calculate the number of beats per second by interpreting intervals on the frequency graph. The data is collected in a table format. They will then use this information to analyze the relationship between the frequency and the number of beats per second.
This Gizmo allows students to explore the sine function in a "real world" application. It can be used as a "hook" to introduce the graph of a sine function or mid unit as a mathematical modeling activity. All 4 activities could be introduced at the same time and worked on continuously or broken apart as a weekly technology activity. The student exploration guide is also available as a word document so the activities can be edited to suit your classroom needs.
This Gizmo also serves as a nice way to show the connection between mathematics and science and can be used as a cross curricula activity. Also, because it is a virtual manipulative which uses both auditory and visual representations, it can meet the needs of diverse learning styles.
Critique
How well does it work?
The Gizmo works well and is "gliche" free. There is both a slider option and a direct input option for entering in the frequency. The frequency of the sliders is restricted to 437-443 Hz, and the time interval is restricted to 4 seconds. The sounds are very close at all of the frequencies provided so students will have to listen very closely and some students may have difficulty hearing any difference in the sounds, however that is basically the purpose of the Gizmo so it is difficult to cite it as a drawback.
Are the written materials well organized and useful?
Like most of the Gizmos on Explore Learning, this Gizmo provides learning materials which consist of a student exploration guide, a teacher guide which provides suggestions for how to implement the applet in a lesson complete with time approximations, disscussion questions and the answers to the student exploration guide, as well as a vocabulary document. Overall the materials are easy to use and well organized.
The student exploration guide does a fairly good job of guiding students through activities on the Gizmo and is broken up into easily digestable parts. Some of the instructions on Activity C were a little cloudy because the students would have to figure out what the "green pinched region" was in order to complete the activity. An accompanying diagram or picture demonstrating what this area was would be helpful. Since all of the materails can be downloaded as a word document and because you can take screenshots of the Gizmo and export them to a word document, teachers can easily edit these materials.
The student exploration guide does a fairly good job of guiding students through activities on the Gizmo and is broken up into easily digestable parts. Some of the instructions on Activity C were a little cloudy because the students would have to figure out what the "green pinched region" was in order to complete the activity. An accompanying diagram or picture demonstrating what this area was would be helpful. Since all of the materails can be downloaded as a word document and because you can take screenshots of the Gizmo and export them to a word document, teachers can easily edit these materials.
What are the purposes and goals of the technololgy? Does the technology reach this goal?
The purpose of this Gizmo is to allow students to listen to sounds at different frequencies using the concept of tuning and to determine how frequency affects the sine function. Students also learn how to determine the difference in frequency of two sounds by analyzing their graphs. The visual graph shows the sine functions of the sounds in two diffreent colors so its easy to compare the graphs and make observations about the graphs over a 4 second interval of time. Students can also see the affects on amplitude when the sounds are palyed together.
Is the technology relatively easy to use?
There is both a slider option and a direct input option for entering in the frequency which is a nice option. There is a time marker which allows the user to manually trace the frquency over time. The buttons and icons are both clearly labeled and easy to use. The pointers are a little finicky but not really a neccessary component of the Gizmo. The "play" buttons are easy to figure out and function properly. The zoom feature was the least identifiable button and may be a little hard to see but Activity C describes its location and use. All of the tools can be turned on or off so students can focus on different apsects of the activity with minimal distractions.
Does the technology enhance or extend the teaching and learning process for the intended mathematics concepts? How and why?
This Gizmo allows students to relate sine functions to a common real world occurance. It also shows the connection between mathematics and science and visually demonstartes the relationship between sinusoidal functions and frequency. The concept of frequency can then be related back to the period of sinusoidal functions.
Would you recommend this product for purchase to a school? Why or why not?
YES!!! Explore Learning provides a plethora of Gizmos for both mathematics and science grades K-12. There is also an iPad app. Teachers can set up classes and create online assignments. There is a 5 question assessment attached to all of the Gizmos and these can be used as either a summative or formative assessment to monitor student progress. There are an abundance of resources provided for the site and included in the teacher guides. Both the technical support and instructional support are excellent.
Standards
Common Core
F.IF.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
CCGPS
MM4A3.b: Determine the characteristics of the graphs of the six basic trigonometric functions.
MM4A3.c: Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.
MM4A3.d: Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.
MM4A3.c: Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.
MM4A3.d: Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.
Standards for Mathematical Practice which were addressed
1: Make sense of problems and persevere in solving them.
2: Reason abstractly and quantitatively.
4: Model with mathematics.
5: Use appropriate tools strategically.
7: Look for and make use of structure
8: Look for and express regularity in repeated reasoning.
2: Reason abstractly and quantitatively.
4: Model with mathematics.
5: Use appropriate tools strategically.
7: Look for and make use of structure
8: Look for and express regularity in repeated reasoning.
Explore Learning Info
![Picture](/uploads/3/1/6/0/31605851/7654802.jpg?250)
Explore Learning provides hundreds of online manipualtors and simulators for grades K-12 in both mathematics and science. Most of the applets have accompanying learning materials which typically include a student exploration guide and a teacher guide which provides suggestions for how to implement the applet in a lesson complete with time approximations, disscussion questions and the answers to the student exploration guide.
A paid subscription is needed for extended use but all of the Gizmos can be previewed for 5 minutes and there is a 30 day free trial. The 30 day free trial allows you to have full access to the site for 30 days so you can set up classes and have students complete online assignments. If a school or district purchases a subscription, training is provided and there is also an account representative assigned who will help teachers create lessons to use in their classrooms.
A paid subscription is needed for extended use but all of the Gizmos can be previewed for 5 minutes and there is a 30 day free trial. The 30 day free trial allows you to have full access to the site for 30 days so you can set up classes and have students complete online assignments. If a school or district purchases a subscription, training is provided and there is also an account representative assigned who will help teachers create lessons to use in their classrooms.
References
The Common Core State Standards Initiative (2011). Common core state standards for mathematics.
Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
Explore Learning (n.d.). Sound beats and sine waves. Retrieved from
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=524
Georgia Department of Education (2006). Mathematics Georgia performance standards.
Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-II-Stds-rev-0409.pdf
Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
Explore Learning (n.d.). Sound beats and sine waves. Retrieved from
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=524
Georgia Department of Education (2006). Mathematics Georgia performance standards.
Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-II-Stds-rev-0409.pdf