Strap a bomb to somebody, and they’ll travel even faster.
If you drop them out of a balloon 28 miles up, all of the parts can go faster than the speed of sound.
It happened to someone recently, I think.
Reminds me of the Dave Barry line – “The fastest animal on earth is a cow that has been dropped out of a balloon.”
Tympanic vibration is the body part being acted upon htough. I though the OP was looking for the body moving of it’s own volition?
If so, what about atrial fibrillation? That’s an incredibly fast muscle twitch. . .
I would vote for the vocal cords - since they vibrate at high frequencies
What about astronauts? The International Space Station moves at an average speed of 4.8 miles per second.
As for the speed of individual body parts, I think it would be the tip of an arm or leg, since when moving them, the free ends move faster (cover more distance); this also means that a person with really long arms or legs can move them “faster” than a shorter person, assuming that the entire arm/leg completes its swing in the same amount of time (but it is harder to swing a longer arm/leg).
But his fingertips would get there slower from his elbow’s point of view. Relatively.
Sperm on the way to the egg - or possibly ejaculate during the launch cycle.
No way. Takes several hours for most sperm to make it several inches to the fallopian tubes.
~28mph. Impressive, but not mindblowing
What about the eye’s pupils? How do they rate? 
The bones in the ear? What about them?
Sperm on the way to the egg - consider the size of the sperm and the distance traveled/time.
A thrown object can have a speed higher then the thrower is moving especially when rotational motion is being converted to linear motion.
Fastest in relation to what? If you throw a punch, your arm moves quite fast compared to the rest of your body. Your heart is stationary, but it certainly expands and contracts and the surface flesh can be moving at quite a rate.
How does the size matter? The distance is short, the time is long.. that means slow. Would apply the same to a pebble or a boulder.
Not a voluntary muscle movement either. The vocal chords vibrate because of the air being pushed through them by the lungs. We mereley control the air flow and the tension of the vocal chords.
I think it’s like Spider-Man supposedly having the “proportionate strength and speed of a spider”*. Or the claims that if ants were humans sized they could lift a ton or walk 40 mph. Of course, that just means that a tiny creature exists in a very different environment with different biological constraints than a human sized one.
*As an aside, just imagine the embarrassment of being exposed to radioactive sperm and becoming Sperm Man. “Sperm-Man! Sperm-Man! Does whatever sperm can!”
Relative speed - from here -
[QUOTE=Science Articles, Scientific Current Events | Popular Science]
Sperm are small, but they’re quick—an individual sperm can wiggle through a space 25 times the length of its body in a single second. (For comparison, a human would have to swim 120 miles per hour to achieve the same relative speed.)
[/QUOTE]
Severus Snape when threatened with shampoo.
Your tongue:)
That’s nothing: I once moved at 0.9999999999999999999999951c. Well, relative to the Oh-My-God Particle, at least.
Not while the evil days come not.
A few years later, many embarrassed Jr High school boys would vote for another part of their anatomy 