Oct 4, 2023
The inverse and reciprocal are not the same thing. An inverse is a function that will take that output of f(x) and give you x. A reciprocal is an expression that is taken to the first negative power. An inverse must be a function. The period isn’t a function in most cases and when it is it’s probably 2pi times the wave number. This means T(w) = 2pi/w. We can also define frequencies this way; F(w) = 2pi*w. If we input F into T we get T(F(w)) = 2pi/(2pi*w) or 1/w this is not w and thus Frequency is not the inverse of period. It is the reciprocal.