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 it represent?

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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 it represent?

Mathematics
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|dw:1444621224019:dw|
Consider the following equation: \[\large y=A cosB \theta\] The amplitude is |A|. The period T is \[\large T=\frac{2 \pi}{B}\]
so time period = 2pi/3

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Substituting 2pi/3 for B we get \[\large T=\frac{2 \pi}{\frac{2 \pi}{3}}=you\ can\ calculate\]
how would i do that
\[\large T=\frac{2 \pi \times3}{2 \pi}=?\]
well 2 pi can cancel eachother out right
Yes, your cancelling idea is correct.
so would it be t= 3/2pi
|dw:1444614205373:dw|
t=3
Correct.
i dont quite understand what answers to a b and c would really be. I understand what we did. I guess i just dont understand what they are asking
would amplitude be 1/4
and by period do they mean time? if so then that cannot be determined
You now have the answer to a and the method for finding the period. The time is in seconds. I have shown you how to find the amplitude, it is |A| in the general equation that I gave you. Yes, the amplitude is 1/4 unit. The equation of the mid line is simply: y = 0.
The maximum value of the cos function is 1, and the minimum value of the cos function is -1. That is why the equation of the mid line is y = 0.
How do I find the period? 2pi and 1/4?
The period T was calculated to be 3 seconds.
how did we get that?
We substituted 2pi/3 for B is the equation \[\large T=\frac{2 \pi}{B}=\frac{2 \pi}{\frac{2 \pi}{3}}=\frac{2 \pi \times3}{2\pi}=3s\]
ohhhh okay! I see how that would be the answer thank you!
You're welcome :)
i just have one question that im kinda confused about, if i did it right. coul you look at it and tell me if I have the right idea
Please post your next question as a new question. Thank you.
alright:)

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