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This is the actual graph. If you add a wave at 5 beats per second and 3 beats per second, you get a weird graph and it would be hard to determine what waves were added. This is why you use the Fourier Transform. It also also normally expressed with complex numbers, but Desmos doesn't have them sadly. You can also change the 5 in the integral and next to it of you want a more precise calculation.
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This is very slow, so you this to see whats happening: https://www.desmos.com/calculator/ywxqicajbv
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An excellent video by 3Blue1Brown showing whats happening: https://www.youtube.com/watch?v=spUNpyF58BY
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