Chapter 4.8, Problem 51E

Solution

a.

To graph: The scatter plot of the sound-pressure.

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 value of a , b , and h and find the sinusoidal model $y=a\sin \left(b\left(t-h\right)\right)$ .

The obtained equation is $y=1.5197\sin \left[2467\left(t-0.002\right)\right]$ .

Given Information:

Refer the given table.

Explanation:

Consider the given information,

Refer the given table.

  

Determine the regression model in the form $y=a\sin \left(b\left(t-h\right)\right)$ by using the calculator.

  $y=1.5197\sin \left[2467\left(t-0.002\right)\right]$

Compare the above model with $y=a\sin \left(b\left(t-h\right)\right)$ .

  $\begin{array}{c}a=1.5197\\ b=2467\\ h=0.002\end{array}$

Now, plot the graph of the equation over the scatter plot.

  

Therefore, the obtained equation is $y=1.5197\sin \left[2467\left(t-0.002\right)\right]$ .

c.

To determine: The frequency of the sinusoidal model.

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

Given Information:

The best fit equation is $y=1.5197\sin \left[2467\left(t-0.002\right)\right]$ .

Explanation:

Consider the given information,

  $y=1.5197\sin \left[2467\left(t-0.002\right)\right]$

Now, compute the frequency.

  $\begin{array}{c}\text{frequency}=\frac{2467}{2\pi }\\ \approx 393\text{ Note }G\end{array}$

Therefore, the required value is $393\text{ Note }G$ .

d.

To determine: The musical note produced by the tuning fork used to create by using the previous part (c).

The obtained frequency is $\text{Note} G$ .

Given Information:

The obtained frequency in previous part (a) is $393\text{ Note }G$ .

Explanation:

Consider the given information,

  $393\text{ Note }G$

According to the Table 4.5,the musical note corresponding to $f\approx 392$ .

Therefore, the musical note is $\text{Note} G$ .