The beat frequency is given by the absolute difference of the two frequencies:
\[
f_{\text{beat}} = |f_1 - f_2|
\]
Given:
\[
f_1 = v - 1, \quad f_2 = v + 2
\]
Now calculate the beat frequency:
\[
f_{\text{beat}} = |(v + 2) - (v - 1)| = |v + 2 - v + 1| = |3| = 3
\]
So, the number of beats per second is:
\[
\boxed{3}
\]