Module 4 - Parametric Equations, Trigonometric and Inverse Trigonometric Functions | ||||||||
Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Lesson 4 | Self-Test | ||||||||
Lesson 4.3: Sine Regression | ||||||||
In the previous lesson you started with an equation and found the corresponding graph by looking at the transformations of the basic graph. A more realistic situation might be to start with a graph of real-world data and then find an equation to fit the data. This can be done on your TI-83 using regression. If the data appear to be sinusoidal, then you can use sine regression. In this lesson you will download data sets produced by a turning fork to your calculator and explore finding the equation that fits the data. Tuning Fork Data A vibrating object that disturbs the surrounding air and causes the air molecules to vibrate produces sound. These vibrations cause a periodic change in air pressure that travels through the air much like ripples on a body of water. The air pressure waves are more commonly called sound waves. Although most sounds are a combination of many different sounds, the sound from a turning fork is a single tone that can be described mathematically using a transformed sine function. A Texas Instruments CBL™ and microphone probe were used to measure a sound wave from a tuning fork. The information in the data will allow you to determine the specific note that was sounded. Downloading the Data to Your Computer
Transferring the Data to the TI-83 Click here to get information about how to obtain the needed cable and to review the procedure to transfer the lists from your computer to your calculator.
![]() Plotting the Data
![]() ![]() Sine Regression Because the graph appears to be a transformed sine function, perform sine regression and store the regression equation.
![]() ![]() After a minute or two a sine equation that fits the data will be displayed on the Home screen and stored in Y1. ![]()
The Forms
Notice that the regression equation is slightly different from the form y = Asin[B(x + C] + D described in Lesson 4.2. A, B and D are the same as the values in the regression equation, but the value of C in the transformed equation is found by dividing the value of C in the regression equation by the value of B. B must be factored out to determine the horizontal shift of the transformed graph. The transformed regression equation has the characteristics listed below.
![]() Period and Frequency
The period of this sine wave is
The Tuning Fork's Note A frequency of 256 cycles per second is the frequency of the note middle C, so the tuning fork must be a "C". 4.3.1 The period is the distance from one peak to the next peak. If another tuning fork were used with a higher frequency than the tuning fork in this lesson, how would its graph compare with the graph above? Write your response then click here for the answer. |
||||||||
< Back | Next > | ||||||||
©Copyright
2007 All rights reserved. |
Trademarks
|
Privacy Policy
|
Link Policy
|