# Finding the period of a periodic function

• October 1st 2011, 10:51 PM
rebghb
Finding the period of a periodic function
Hello Everyone!

I think my question would go here. Is there a method to find the period of a given periodic function? Say: $f(t)=\cos (2\pi f_a t)\cos (2\pi f_b t)$ where b is not necessarily an integer multiple of a

Thanks!
• October 5th 2011, 07:45 AM
BookEnquiry
Re: Finding the period of a periodic function
Is this anything to do with wiki: Beat (acoustics)?

2 cos (2丌f at) cos (2丌f bt) = cos (2丌f a -2丌f b)t + cos (2丌f a +2丌f b)t

f beat = f1 - f2

f beat = (f a +f b) - (f a - f b) = 2f b

period, T = 1/(2f b)? Is it?
• October 5th 2011, 11:10 AM
CaptainBlack
Re: Finding the period of a periodic function
Quote:

Originally Posted by rebghb
Hello Everyone!

I think my question would go here. Is there a method to find the period of a given periodic function? Say: $f(t)=\cos (2\pi f_a t)\cos (2\pi f_b t)$ where b is not necessarily an integer multiple of a

Thanks!

This is not periodic unless $(f_a+f_b)/(f_a-f_b)$ is a rational number. If this ratio is rational the period of $f(t)$ can be found by writing it in canonical form

CB