## anonymous one year ago 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?

1. anonymous

|dw:1444621224019:dw|

2. kropot72

Consider the following equation: $\large y=A cosB \theta$ The amplitude is |A|. The period T is $\large T=\frac{2 \pi}{B}$

3. anonymous

so time period = 2pi/3

4. kropot72

Substituting 2pi/3 for B we get $\large T=\frac{2 \pi}{\frac{2 \pi}{3}}=you\ can\ calculate$

5. anonymous

how would i do that

6. kropot72

$\large T=\frac{2 \pi \times3}{2 \pi}=?$

7. anonymous

well 2 pi can cancel eachother out right

8. kropot72

Yes, your cancelling idea is correct.

9. anonymous

so would it be t= 3/2pi

10. kropot72

|dw:1444614205373:dw|

11. anonymous

t=3

12. kropot72

Correct.

13. anonymous

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

14. anonymous

would amplitude be 1/4

15. anonymous

and by period do they mean time? if so then that cannot be determined

16. kropot72

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.

17. kropot72

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.

18. anonymous

How do I find the period? 2pi and 1/4?

19. kropot72

The period T was calculated to be 3 seconds.

20. anonymous

how did we get that?

21. kropot72

We substituted 2pi/3 for B is the equation $\large T=\frac{2 \pi}{B}=\frac{2 \pi}{\frac{2 \pi}{3}}=\frac{2 \pi \times3}{2\pi}=3s$

22. anonymous

ohhhh okay! I see how that would be the answer thank you!

23. kropot72

You're welcome :)

24. anonymous

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

25. kropot72