Question

5. A sound wave is modeled with the equation y = 1/4 cos 2pi/3 ∅

a.) Find the period. Explain your method.
b.) Find the amplitude. Explain your method.
c.) What is the equation of midline?

Answer 1

QUESTION A

The sound wave is modeled by;

`(1)/(4)\cos((2\pi)/(3)\theta)`

This function is of the form;

`y=A\cos(Bx)`, where
`B=(2\pi)/(3)`.

The period is given by;

`T=(2\pi)/(B)`

We substitute the value of B to get;

`B=(2\pi)/((2\pi)/(3) )`

The period is 3.

QUESTION B

The amplitude of the given function is
`|A|`

Comparing the given function to
`y=A\cos(Bx)`,
`A=(1)/(4)`.

The amplitude is
`|(1)/(4)|=(1)/(4)`.

QUESTION C.

The equation of the mid-line is given by;

`y=(1)/(2)(maximum\:value+\:minimum\:value)`

`y=(1)/(2)((1)/(4)+(-1)/(4))`

`y=0`