Wavenumber of corresponding isotope peak in IR?

[magnesium12]

Homework Statement

The infrared spectrum of CO shows a vibrational absorption peak at 2170 cm^-1
(a) What is the force constant of the CO bond?
(b) At what wavenumber would the corresponding peak for
¹⁴CO occur?

Homework Equations

k=ω²μ = (2πcv)²μ

The Attempt at a Solution

So I solved part a correctly and the force constant for CO = 1900N/m
For part b I assumed the force constant was the same for both isotopes so :
v₁₂(√μ₁₂/μ₁₄) = v₁₄
I got v₁₄ = 2079cm^-1. However, the posted answer is 2083cm^-1.
I realize this isn't a very big difference, but I can't see a reason why my answer shouldn't be exact if I'm using the exact wavelength given and amus for the reduced mass (as in 12 and 14 for C, and 16 for O). So am I incorrect in assuming the force constants are the same? If the force constant is different for the isotopes, how would I go about solving this question since I would have two unknowns (k₁₄ and v₁₄).

 

[mfb]

Could be a rounding error.
How did you calculate the reduced masses?

The force constant should be the same.