Far field acoustic pressures from the unsteady motion of the three-dimensional vortex filament are calculated numerically. An accurate numerical scheme for vortex filament motion is also developed and validated. An elliptic vortex ring is a typical example of the three dimensional vortex filament, and it is generated from the elliptic jet exit. An elliptic vortex ring emits a strong sound signal due to significant distortion and stretching of the vortex filament. At the far field, the acoustic pressure is linearly dependent on the third time derivatives of the vortex positions. Therefore, a numerical scheme of high resolution is employed to describe in detail the elliptic vortex ring motions which are highly nonlinear. Discretized vortex filaments are interpolated by using a parametric blending function to remove a possible numerical instability, and the accuracy and efficiency of the scheme are validated by comparisons with the analytic solution of circular vortex ring interaction. Acoustic signals from the evolution of a single elliptic vortex ring are obtained with various aspect ratios of the axes. The calculated periods in the acoustic signals depend to a significant degree on the initial aspect ratio of the ring. The far field acoustic signals depend significantly on increasing the aspect ratio of the elliptic ring.