Chapter 5.PS, Problem 4PS

To determine

a)

To find:

The sine components $p_n\left(t\right)$ and graph the components of the sound wave using graphing utility and then to verify the graph of p for the sound wave modeled by $p\left(t\right)=\frac{1}{4\pi }\left[p_1\left(t\right)+30p_2\left(t\right)+p_3\left(t\right)+p_5\left(t\right)+30p_6\left(t\right)\right]$, with $p_n\left(t\right)=\frac{1}{n}\sin \left(524n\pi t\right)$.

To determine

b)

To find:

The period of each sine component of p and to determine whether p is periodic and to find the period for the sound wave modeled by $p\left(t\right)=\frac{1}{4\pi }\left[p_1\left(t\right)+30p_2\left(t\right)+p_3\left(t\right)+p_5\left(t\right)+30p_6\left(t\right)\right]$, with $p_n\left(t\right)=\frac{1}{n}\sin \left(524n\pi t\right)$.

To determine

c)

To find:

The t – intercepts of the graph of p over one cycle using the graphing utility for the sound wave modeled by $p\left(t\right)=\frac{1}{4\pi }\left[p_1\left(t\right)+30p_2\left(t\right)+p_3\left(t\right)+p_5\left(t\right)+30p_6\left(t\right)\right]$, with $p_n\left(t\right)=\frac{1}{n}\sin \left(524n\pi t\right)$.

To determine

d)

To find:

The absolute maximum and absolute minimum values of p over one cycle using graphing utility for the sound wave modeled by $p\left(t\right)=\frac{1}{4\pi }\left[p_1\left(t\right)+30p_2\left(t\right)+p_3\left(t\right)+p_5\left(t\right)+30p_6\left(t\right)\right]$, with $p_n\left(t\right)=\frac{1}{n}\sin \left(524n\pi t\right)$.