In this work, a low-frequency acoustic sensing scheme is proposed based on the structure of in-fiber Mach-Zehnder interferometer , in which the refractive index difference between fiber core and cladding is used to form 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 itself in interference spectrum shifts, enabling the effective detection of low-frequency acoustic signals through demodulating the spectrum variations. In the paper, the theoretical framework for the acoustic sensing system is derived and validated experimentally. The 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 $267.9{\text{ μPa/H}}{{\text{z}}^{{{1/2}}}}$at 65 Hz. In a frequency range of 50–500 Hz, the system exhibits good acoustic response, with an SNR consistently above 40 dB and a relatively flat signal output. This scheme significantly enhances the acoustic response capability of the sensing system, enabling the effective detection of low-frequency acoustic waves. Additionally, it features simple fabrication and low cost, showing great potential for the development of acoustic wave detection applications.