We demonstrate a new acousto-optic Mach-Zehnder interferometer (MZ) based on a hollow core fiber (HCF). The fabricated acousto-optic device excites two MZs in a 7.5 cm long HCF. In the first MZ, the HCF is attached in a centrally positioned acoustic driver, exciting two acoustically induced long period gratings. The second MZ induces two strong curvatures at the edges of the attached HCF-driver length. The MZs tune the free spectral range of the modulated multiwavelength spectrum by changing the driver's frequency in steps of 1 Hz while providing compactness, efficiency, and high sensitivity, suitable for dynamic filters and fiber sensors.