A piano string is, again, a pendulum in disguise — just a vibrating one instead of a swinging one.
Short, thin, tightly-strung strings (the piano's high notes) vibrate at a high frequency. Long, thick, loosely-strung strings (the low notes, wound in copper wire) vibrate at a low frequency.
Short and light vibrates fast; long and heavy vibrates slow — the exact same rule that separated a hummingbird's wing from an elephant's leg.