Actually, the speed of sound on a standard day at sea level is 1116 FPS. Standard day conditions are at 59F and 29.92 inches Hg. The speed of sound will drop to 1000 FPS at about 30000ft altitude, where the air temp is about -50F and pressure is about 8.9 inch of HG.
When a bullet transitions from above Mach 1 to below Mach, there is a definite tendency to yaw, almost the same as an aircraft. But while an aircraft's nose will yaw back and forth, with a little bobbing in there (Dutch Roll), a bullet has a high rotational component to it's flight, which causes the bullet to corkscrew thru the air. I think the bullets ballistic coefficient has something to do with the amount of yaw, but not sure.
Basically, for best accuracy, you want the bullet to stay either above or below the speed of sound from muzzle to target. But best accuracy is relative. 520 gn bullets from my 45-70 start out at 1300 fps. at 100 yds, they're still above the speed of sound and hold about 1.5 MOA. Testing at 500 yds, where the bullet is way below the speed of sounds shows that the 1.5 MOA still holds, as I can produce groups (occasionally) at that range of about 81/2 - 9 inches, if I do my part. But usually, they're around 10 to 12 inches.