Question

A sound wave is modeled with the equation y=1/4cos2pi/3theta

a. Find the period. Explain your method.
b. Find the amplitude. Explain your method.

Answer 1

given a general equation cos(bx)

the period is

\[\frac{2\pi}{b}\]

in your equation the value of b is

\[b = \frac{2\pi}{3}\]

substitute it to find the period of the curve

Answer 2

wait so would it be 2.09?

Answer 3

@campbell_st

Answer 4

well its

\[period = (2\pi) \div \frac{2\pi}{3}\]

Answer 5

I put it in the calc and it says 3.

Answer 6

well thats the period.... the curve completes 1 full cycle over a distance of 3 units.

now the amplitude

the general form is

y =acos(bx)

a is the amplitude... which is furthest distance the curve moves from its centre.

so looking at your curve

y = 1/4cos(2pi/3 x)

what do you think the amplitude is?

Answer 7

uhh.. I'm so bad at this I don't know.. -1/8?? Idk @campbell_st

Answer 8

a = 1/4 so thats the amplitude.....

amplitude is always the number infront of the trig ratio...

if no number is written the amplitude is 1.

Answer 9

Ohhh yeah, that's right. Thanks so much for your help!