Why Does a Tuning Fork Give an Almost Pure Pitch?

A tuning fork is often said to produce a “pure tone”. More precisely, striking it excites several modes at first, but the fork shape leaves most of the energy in the fundamental. Its higher modes are far removed from that frequency and fade quickly. Once the brief metallic impact has passed, the ear mainly hears one stable pitch close to a sine wave.

In the principal mode, the two tines move in opposite directions and their junction is near a vibration node, so holding the stem does not immediately damp the motion. Yet purity does not mean loudness. Steel transfers sound inefficiently to air, and radiation from the two tines partly cancels. A fork held in free air is therefore quiet. Pressing its stem against a wooden table or resonator lets a much larger surface move, increasing volume without changing the pitch itself.

That clean, stable tone is useful for tuning. Sound the fork together with a piano string or another instrument, and a small frequency difference produces beats: a regular rise and fall in loudness. The tuner listens for those beats to slow and disappear. The fork matters not because its tone is musically rich, but because it removes much of the timbral clutter and makes a pitch difference easier to judge. Listen for the brief impact noise, then the thin, steady principal tone that remains.

https://americanhistory.si.edu/acoustics/tuning-forks
https://www.physicsclassroom.com/mmedia/waves/tfl.cfm