This paper proposes a low-frequency acoustic sensing scheme based on an in-fiber Mach-Zehnder interferometer structure. The structure utilizes the refractive index difference between fiber core and cladding, forming a miniature Mach-Zehnder interferometer through fusion splicing of specialty optical fibers in a multi-mode-ultra-high numerical aperture-multi-mode configuration. This design achieves modal recombination between cladding and core modes, thereby effectively enhancing fiber bending sensitivity. The interferometer structure is then combined with a polyethylene terephthalate (PET) transducer diaphragm, enabling the sensing fiber to undergo curvature changes synchronously with the diaphragm under sound pressure, thereby indirectly increasing the area over which the fiber receives the acoustic field. When external acoustic pressure induces bending modulation on both the sensing fiber and transducer diaphragm, the differential strain distribution between the fiber cladding and core generates an optical path difference. This manifests as interference spectrum shifts, enabling effective detection of low-frequency acoustic signals through demodulation of the spectral variations. The paper derives the theoretical framework for the acoustic sensing system and validates it through experiments. Results show that at 65 Hz, the system achieves a signal-to-noise ratio (SNR) of approximately 57 dB and a minimum detectable sound pressure of 267.9 μPa/Hz^1/2@65 Hz. Within the frequency range of 50 Hz-500 Hz, the system demonstrates good acoustic response, with a SNR consistently above 40 dB and relatively flat signal output. This scheme significantly enhances the acoustic response capability of the sensing system, enabling effective detection of low-frequency acoustic waves. Additionally, it features simple fabrication and low cost, showing great potential for development in acoustic wave detection applications.