Answered

Engage with knowledgeable experts and get accurate answers on IDNLearn.com. Discover reliable and timely information on any topic from our network of experienced professionals.

The sound wave of two music notes can be represented by the function y = 2cos2x and y = −cos x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?

x = 0°, 60°, 180°, 300°
x = 0°, 120°, 240°, 180°
x = 60°, 90°, 270°, 300°
x = 90°, 120°, 240°, 270°

Sagot :

MrRoyalidn

The sound waves are illustrations of cosine functions

The frequencies of the sound waves are x = 90°, 120°, 240°, 270°

How to determine the frequencies of the sound waves

The equations of the sound waves are given as:

[tex]y = 2\cos^2(x)[/tex]

[tex]y =-\cos(x)[/tex]

Next, we plot the graphs of the functions [tex]y = 2\cos^2(x)[/tex] and [tex]y =-\cos(x)[/tex]

From the graphs of the functions (see attachment), we have the following x-coordinates of the points of intersection of the both curves between the interval [0°, 360°)

[tex]x =(\frac{\pi}{2},\frac{2\pi}{3},\frac{4\pi}{3},\frac{3\pi}{2})[/tex]

Express as degrees

[tex]x =(90^o,120^o, 240^o, 270^o)[/tex]

Hence, the frequencies of the sound waves are x = 90°, 120°, 240°, 270°

Read more about sound waves at:

https://brainly.com/question/2285154

View image MrRoyal
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.