We propose and demonstrate a modified phase-generated carrier (PGC) demodulation scheme optimized for detection of ultrasound using interferometric sensors with sinusoidal fringes. The sensor used in demonstration is made from a pair of weak fiber Bragg-gratings at the ends of a coiled fiber that form a low-finesse Fabry-Perot interferometer. The phase of the laser source is modulated using an electro-optic phase modulator to generate the carrier signal and obtain 2 quadrature (the sine and cosine) terms at the first and the second order carrier frequencies. The signal of interest (ultrasound) has much higher frequency than the environmental perturbation but a very small amplitude that causes only small phase shift. Using small-signal approximation, for each of the 2 quadrature terms, we separate the contributions from the environmental perturbations (quasi-DC component) and from the ultrasound (AC component). The AC components that contain the information of the ultrasound signal are then further amplified with a large gain. The signal of interest is constructed by simple algebraic operations on the 2 quasi-DC components and the 2 amplified AC components involving multiplying and summing. This work provides a simple and robust demodulation method with potentially high sensitivity for fiber-optic interferometric ultrasound sensors.