Abstract
Hara's formula is used to predict the pressure rise of a compression wave generated by a high-speed train entering a tunnel. The acoustic theory is used to predict its waveform. Hara's formula was derived from the shock theory. Meanwhile, the acoustic theory produces the same non-dimensional formula as Hara's formula up to order OM4, where M is the train Mach number, when the non-linear acoustic effect in the vortex sound theory is considered. However, the relationship between the shock and acoustic theories remains unclear because the closed formula produced by the vortex sound theory apparently differs from that of Hara's formula. This study shows that Hara's formula can be deductively obtained from the non-linear acoustic theory. A general equation used to predict the compression waveform with a relative error of Op/ρ0c02, where p/ρ0c02 is the non-dimensional acoustic pressure to the atmospheric density ρ0 and the sound speed c0, is shown herein using the non-linear acoustic theory.
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