Developing an Understanding for

the Function F(x)=Acos(B(x-C))+D or G(x)=Asin(B(x+c))+D


Using the CBL and Texas Instrument Calculators
my classes collected data on the
sound wave of various tuning forks. (Directions)

After collecting the data the students
then used their knowledge of the constants
in the equation
y=Acos(B(x-C))+D
to fit a curve to the data.

The students searched
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for various peaks and valleys in the graph to determine A: the Amplitude

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the x displacement for one period of the graph to determine B

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the shift of the graph from the y-axis to determine C the shift, and

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the amount of vertical shift to determine D

   


After collecting the data the students determined the frequency of the tuning fork using their equation.
With the equation they fit the graph most students
found that their experimental data had generated
a frequency which only had an error of less than 5%.