Abstract: Acoustic negative refraction with backward-wave (BW) effects have been both theoretically and experimentally established in the second band of a two-dimensional (2D) triangular sonic crystal. Intense Bragg scattering results in extreme deformation of the second band equifrequency surface (EFS) into two classes: one around the K point and the other around the Γ point of the reduced Brillouin zone. The two classes can both lead to BW negative refraction but with reverse negative refraction dependence on frequency and incident angle. Not only BW negative refraction but also BW positive refraction can be present at equifrequency surfaces around the K point, so it is possible to enhance the resolution of acoustic waves beyond the diffraction limit regardless of refraction. This has no analogy in either left-handed materials or the first band of sonic crystals. These characteristics make refraction in the second band quite unique.