  We consider cigar shaped Fermi superfluid in the BEC-BCS crossover. Using
polytropic form of equation of state, we derive low energy multibranch bosonic
excitations and the corresponding density fluctuations in three different
regimes along the crossover, namely weak-coupling BCS, unitarity and molecular
BEC regimes. Bragg spectroscopy can be used to probe the multibranch nature of
the low energy bosonic excitations by measuring dynamic structure factor.
Therefore, we calculate dynamic structure factor in those three different
regimes. In the Bragg spectroscopy, an actual observable is momentum imparted
to the superfluid due to the Bragg potential. We also present results of the
momentum imparted to the superfluid due to the Bragg pulses.
