Question

A sound wave is modeled with the equation y= 1/4 cos 2π/3 θa. Find the period. Explain your method.b. Find the amplitude. Explain your method

Answer 1

The cosine function is expressed as:

`y=Acos(w\theta)`

Where A is the amplitude and w is the angular frequency.

The period of a wave is given by:

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

We are given the equation:

`y=(1)/(4)cos\left((2\pi)/(3)\theta\right?\text{ }`

By comparison, we have:

`A=(1)/(4),\text{ }w=(2\pi)/(3)`

Calculate the period:

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

a. The period is T = 3

b. The amplitude is 1/4