Question

A particular sound wave can be graphed using the function `y=-3sinx`, how do you find the period of the function?

Answer 1

I got: `T=2pi`

Explanation:

For the case of a sound wave I would prefer to "see" it as a displacement along `y` as function of time. In general the form of the wave would be:

`y(t)=Asin(omegat)` Function of `t`

where in your case you have:

`y(x)=-3sin(1x)` Function of `x`

although this may seem a bit strange and difficult it allows you to "see" the various components of your wave:

`A` is the amplitude or the maximum reached by the displacement of your wave that in your case is `3` (the minus tells you that at the start the sine wave will be "upside down" compared to a normal sine).

`omega` is a number that tells you the "speed" of your wave in terms of radians per seconds or:

`omega=(2pi)/T` where `T` is the period.

In your case `omega=1` so that:
`(2pi)/T=1`
and
`T=2pi` so that the period will be `2pi`

We can "see" this wave graphically:
graph{-3sin(x) [-10, 10, -5, 5]}