  We develop a stochastic mean-field theory to describe active frequency
measurements of pulsed superradiant emission, studied in recent experiments
with strontium-87 atoms trapped in an optical lattice inside an optical cavity
[M. Norcia, et al., Phys. Rev. X 8, 21036 (2018)]. Our theory reveals the
intriguing dynamics of atomic ensembles with multiple transition frequencies,
and it reproduces the superradiant beats signal, noisy power spectra, and
frequency uncertainty in remarkable agreement with the experiments. Moreover,
by reducing the number of atoms, elongating the superradiant pulses and
shortening the experimental duty cycle, we predict a short-term frequency
uncertainty $9\times10^{-16} \sqrt{\tau/s}$, which makes active frequency
measurements with superradiant transitions comparable with the record
performance of current frequency standards [M. Schioppo, et al., Nat.
Photonics, 11, 48 (2017)]. Our theory combines cavity-quantum electrodynamics
and quantum measurement theory, and it can be readily applied to explore
conditional quantum dynamics and describe frequency measurements for other
processes such as steady-state superradiance and superradiant Raman lasing.
