Fiber optic sensing technology's performance is crucially influenced by the choice of demodulation algorithms. Traditional intensity demodulation methods rely on precisely controlling the working point to the quadrature point (Q point) by adjusting the laser wavelength. However, issues like laser wavelength adjustment accuracy and laser power variations with wavelength affect demodulation accuracy, limiting its application in complex scenarios. Additionally, this method requires sensitivity calibration and has a limited dynamic range. To address these limitations, this paper proposes an amplitude ratio of harmonic components (ARHC) demodulation algorithm. It analyzes the harmonic components of the interference light intensity output by the sensor to calculate Fabry-Perot cavity length changes, achieving real-time demodulation of dynamic signals. Compared to traditional methods, the ARHC algorithm simplifies system adjustment, has a larger demodulation range and higher accuracy, and is more adaptable to environmental changes. Simulations and experiments demonstrate its effectiveness and high-precision, large-dynamic-range signal demodulation capabilities under different interference conditions. The EFPI ultrasonic sensitivity based on the ARHC algorithm is 2.5 nm/Pa@23kHz, and it can linearly demodulate up to a vibration amplitude of 372.8 nm for the sensitive diaphragm, with a demodulation error of less than or equal to 0.8 nm.