The inelastic neutron scattering spectra of the polycrystalline n-alkanes, 5 < n < 25, have been obtained at similar to 25 K. At this temperature the n-alkane molecules are extended in their all-trans configuration. The spectral region from 200 to 600 cm(-1) is reported with emphasis on the higher frequency longitudinal acoustic modes (LAM). These modes are identified by their nominal translational symmetry eigenvector, kappa. A complete assignment of experimental frequencies out to kappa approximate to 0.7 is presented for the first time. This assignment is consistent with the known optical data and ab initio Hartree-Fock and DFT calculations. On the basis of these theoretical results, the lower frequency, higher kappa LAM modes are also assigned. The LAM sequences exhibit bandhead behavior, i.e., a maximum frequency value, upsilon(max), at some value of kappa. The maximum frequency is consistently found at kappa(max)=0.36+/-0.01 [cf. polyethylene (PE), kappa(max)=0.34] for all chain lengths but the value of the maximum frequency, upsilon(max), increases roughly linearly with n for n > 7. At about n=21 it reaches the value found for PE, 525 cm(-1). This variation in frequency with chain length for the same nominal value of kappa and also the full set of calculated DFT LAM results is compared with the expectations of a simple zig-zag bead bending model.