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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 :

MrRoyal

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
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