# Correct my frequency/period conversion (please)

• Apr 27th 2011, 05:27 PM
MSUMathStdnt
Is frequency the inverse of period, or is it 2pi/period?

If you have an equation like this, A*sin(fx-p), or A*cos(fx-p), then f is the frequency (A is amplitude, p is phase shift). Allegedly, the period is T=2pi/f. Supposedly, frequency is f=1/T. Does anyone see anything wrong here (e.g, substituting 1/T for f in the equation for T does not yield T)?

For example y=sin(2t). Frequency f=2. Period T=2pi/f=2pi/2=pi (this matches my calculator which shows one cycle every pi). So, of course, f=1/T=1/Pi, except that f=2. What's the deal?
• Apr 27th 2011, 05:37 PM
topsquark
Quote:

Originally Posted by MSUMathStdnt
Is frequency the inverse of period, or is it 2pi/period?

If you have an equation like this, A*sin(fx-p), or A*cos(fx-p), then f is the frequency (A is amplitude, p is phase shift). Allegedly, the period is T=2pi/f. Supposedly, frequency is f=1/T. Does anyone see anything wrong here (e.g, substituting 1/T for f in the equation for T does not yield T)?

For example y=sin(2t). Frequency f=2. Period T=2pi/f=2pi/2=pi (this matches my calculator which shows one cycle every pi). So, of course, f=1/T=1/Pi, except that f=2. What's the deal?

Yeah, you have to be wary of context. By definition frequency is the inverse of the period, f = 1/T, and angular frequency $\displaystyle \omega$ is 2 $\displaystyle \pi$ / T. The problem is that a lot of texts use f for the angular frequency.

Sometimes you get a break and you are given the unit for "frequency" as rad/s. The "rad" is a give-away for angular frequency.

-Dan