How do musical frequencies relate to the numbers in this signal decomposition?

[bobsmith76]

My book reads

step 1 = 2 cos(654πt)cos(-130πt)
step 2 = 2 cos(2 * 327 * π * t)cos(130πt)
step 3 = f₂ - f₁ = 392 - 262 = 130 Hz

t = seconds
π = pi

I don't see how they get from step 1 to step 2, nor do I understand how they get from step 2 to step 3.

 

[uart]

I don't see how they get from step 1 to step 2

654 = 2*327, and cos() is an even function.

 

[bobsmith76]

ok, where did the numbers 392 and 262 come from? What happened to pi?

 

[uart]

ok, where did the numbers 392 and 262 come from? What happened to pi?

Frequency (in Hz) is equal to the radian frequency divided by 2 pi.

cos(a-b) + cos(a+b) = 2 cos(a) cos(b)

You are given the "a" and the "b" and you need to find the corresponding "a+b" and "a-b" of the decomposed (into individual cosine wave) signal.