Belt Frequency = 2*pi*R1*F1 / BeltLength
F1 = frequency of rotation of larger pulley
BeltLength ~ 2*C + 2*1.57*(R1+R2)+[(R1-R2)^2]/C
C = center-to-center distance between pulleys
R1 = radius of smaller pulley, R2 = radius of larger pulley
"Belt Frequency" above is inverse of the time it takes the belt to travel rotate once. It is not the belt natural frequency.
See attached for derivation of an alternate calculation of belt length
* Edited to correct the message/attachment by dividing the last term of the belt length equation by C