In this paper, a numerical method is proposed for investigating the flow-induced vibration (FIV) and acoustically induced vibration (AIV) of a straight pipe with an orifice plate. First, the turbulent pressure (TP) and acoustic pressure (AP) signals on the pipe wall were obtained through the simulation of an unsteady flow field and the application of Mohring's analogy, respectively. Subsequently, the FIV and AIV of the pipe were calculated by means of one-way fluid-structure interaction and acoustic-structure interaction, respectively. The calculated pressures, flow velocities, and sound powers at the monitoring point were in good agreement with the experimental results reported in the literature. The numerical results revealed that the power spectral densities of the AP were significantly higher than those of the TP on the surface of the tested end pipe, particularly at the natural frequencies of the acoustic modes. In the low-frequency regime, FIV was the dominant factor, whereas in the medium-high frequency regime, particularly above the cutoff frequency of the plane wave, AIV was the dominant factor. The findings of the parametric studies demonstrated that the AP and AIV of the pipe exhibited a considerable increase with the Mach number. Conversely, the TP and FIV demonstrated a more pronounced rise when the Mach number increased from 0.1 to 0.2, followed by a less pronounced increase when the Mach number increased from 0.2 to 0.3. A reduction in the orifice diameter resulted in an increase in the AP and AIV. In contrast, the TP and FIV exhibited a comparatively minor increase.