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

Sep 29, 2017

a. The period is $3$
b. The amplitude is $\frac{1}{4}$

#### Explanation:

a. The period of trigonometric functions are as follows.
f(x) = sin(aθ) or f(x) = cos(aθ) -> The period is $\frac{2 \pi}{a}$
f(x) = tan(aθ)  -> The period is $\frac{\pi}{a}$

In the equation $y = \frac{1}{4} \cos \left(\frac{2 \pi}{3} \theta\right)$, $a$=$\frac{2 \pi}{3}$,
so the period is $\frac{2 \pi}{\frac{2 \pi}{3}} = 3$.

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 $y = \frac{1}{4} \cos \left(\frac{2 \pi}{3} \theta\right)$ is $\frac{1}{4}$.

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

The equation $y = \frac{1}{4} \cos \left(\frac{2 \pi}{3} \theta\right)$ is a trigonometric function.
If you prot $\theta$ and $y$ on a plane you will see a wave-shaped graph.