QUESTION A
The sound wave is modeled by;
[tex]\frac{1}{4}\cos(\frac{2\pi}{3}\theta)[/tex]
This function is of the form;
[tex]y=A\cos(Bx)[/tex], where [tex]B=\frac{2\pi}{3}[/tex].
The period is given by;
[tex]T=\frac{2\pi}{B}[/tex]
We substitute the value of B to get;
[tex]B=\frac{2\pi}{\frac{2\pi}{3} }[/tex]
The period is 3.
QUESTION B
The amplitude of the given function is [tex]|A|[/tex]
Comparing the given function to [tex]y=A\cos(Bx)[/tex], [tex]A=\frac{1}{4}[/tex].
The amplitude is [tex]|\frac{1}{4}|=\frac{1}{4}[/tex].
QUESTION C.
The equation of the mid-line is given by;
[tex]y=\frac{1}{2}(maximum\:value+\:minimum\:value)[/tex]
[tex]y=\frac{1}{2}(\frac{1}{4}+\frac{-1}{4})[/tex]
[tex]y=0[/tex]
