Question

I've been struggling in this sound wave question for more than 30min, can someone help me please?

Answer 1

a. The period is `3`
b. The amplitude is `1/4`
c. Sorry, I wasn't able to explain clearly. Please help.

Explanation:

a. The period of trigonometric functions are as follows.
`f(x) = sin(aθ) or f(x) = cos(aθ)` -> The period is `(2pi)/a`
`f(x) = tan(aθ)` -> The period is `(pi)/a`

In the equation `y=1/4cos((2pi)/3theta)`, `a`=`(2pi)/3`,
so the period is `(2pi)/((2pi)/3)=3`.

b. The amplitude is the maximum absolute value of the wave.
For `sin` or `cos` functions, the amplitude is the coefficient before
the trigonometrics.Therefore the amplitude for `y=1/4cos((2pi)/3theta)` is `1/4`.

c. The equation of a function is a relationship between the variables.
For example, `y=2x` is an equation, and this means `y` is
proportional to `x`.

The equation `y=1/4cos((2pi)/3theta)` is a trigonometric function.
If you prot `theta` and `y` on a plane you will see a wave-shaped graph.