Question

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

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: $T = 2 \pi$

#### 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:

$y \left(t\right) = A \sin \left(\omega t\right)$ Function of $t$

where in your case you have:

$y \left(x\right) = - 3 \sin \left(1 x\right)$ 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:

$\omega = \frac{2 \pi}{T}$ where $T$ is the period.

In your case $\omega = 1$ so that:
$\frac{2 \pi}{T} = 1$
and
$T = 2 \pi$ so that the period will be $2 \pi$

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

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