Question

A sound wave is modeled with the equation y= 1/4 cos 2pi/3 theta.
A. Find the period. Explain your method.
B. Find the amplitude. Explain your method.
C. What is the equation of the midline? What does is represent?

Answer 1

\[y=\frac{ 1 }{ 4} \cos \frac{ 2\pi }{ 3 } \]theta

Answer 2

In the equation
\[\large y=A \cos(Bx)\]
the period T is given by
\[\large T=\frac{2\pi}{B}\]
and the amplitude is absolute value of A = |A|
You need to plug the values into the above to find the values of the period and the amplitude.

Answer 3

In your equation
\[\large B=\frac{2\pi}{3}\]
and |A| = 1/4

Answer 4

So the period is T= 2pi/3 and the amplitude is 1/4?

Answer 5

The amplitude is 1/4.
The period is given by
\[\large T=\frac{2\pi}{\frac{2\pi}{3}}\]

Answer 6

So that's the period, the amplitude is 1/4. How do we find the midline cuz i have to show my work

Answer 7

\[\large T=\frac{2\pi}{\frac{2\pi}{3}}=\frac{2\pi}{1}\times\frac{3}{2\pi}=?\]

Answer 8

3?

Answer 9

Correct, the period is 3 units.
There is no y-shift, therefore the equation of the midline is y = 0

Answer 10

The equation y = 0 is simply the x-axis.

Answer 11

How do we find the midline though? @kropot72

Answer 12

@UsukiDoll

Answer 13

@Astrophysics

Answer 14

As I posted previously
"There is no y-shift, therefore the equation of the midline is y = 0"
"The equation y = 0 is simply the x-axis."