Chapter 4.8, Problem 43E

Solution

a.

To graph: The scatter plot of the given data $\left[0,0.0062\right]$ by $\left[-0.5,1\right]$ viewing window.

Given Information:

The tables is defined as,

  

Explanation:

Consider the given table,

  

Now, use graphing calculator to make the scatter plot and set the given window.

  

Therefore, the above graph is the required graph.

b.

To determine: The correct equation that appears good to the above model I part (a).

The first equation is the best feet equation.

Given Information:

The equations are defined as,

  $\begin{array}{c}\text{i}.y=0.6\sin \left(2464x-2.84\right)+0.25\\ \text{ii}.y=0.6\sin \left(1210x-2\right)+0.25\\ \text{iii}.y=0.6\sin \left(2440x-2.1\right)+0.15\end{array}$

Explanation:

Consider the given information,

  $\begin{array}{c}\text{i}.f\left(x\right)=0.6\sin \left(2464x-2.84\right)+0.25\\ \text{ii}.g\left(x\right)=0.6\sin \left(1210x-2\right)+0.25\\ \text{iii}.h\left(x\right)=0.6\sin \left(2440x-2.1\right)+0.15\end{array}$

Draw all the given equation over the scatter plot. So,

  

Therefore, the obtained equation is $f\left(x\right)=0.6\sin \left(2464x-2.84\right)+0.25$ .

c.

To determine: The approximate frequency of the tuning fork.

The obtained frequency is $392\text{ oscillations/sec}$ .

Given Information:

The best fit equation is $y=0.6\sin \left(2464x-2.84\right)+0.25$ .

Explanation:

Consider the given information,

  $y=0.6\sin \left(2464x-2.84\right)+0.25$

Now, compute the frequency.

  $\begin{array}{c}\text{frequency}=\frac{2464}{2\pi }\\ \approx 392\text{ oscillations/sec}\end{array}$

Therefore, the required value is $392\text{ oscillations/sec}$ .