Yes, when playing the piano, the sound of each key corresponds to a specific frequency of sound. The piano is a tuned instrument where each key represents a distinct pitch.
The pitch of a piano key is determined by the frequency at which the corresponding piano string vibrates when struck by the piano hammer. When you press a key on the piano, it activates a mechanism that causes a felt-covered hammer to strike the corresponding string(s). The length, tension, and mass of each string determine its specific fundamental frequency.
In a standard modern piano, there are 88 keys, starting from the lowest note, A0, to the highest note, C8. Each key represents a different frequency, and the frequency doubles as you move up an octave. For example, the A above middle C, known as A4, is typically tuned to vibrate at a frequency of 440 Hz, which is a standard pitch reference known as "A440."
As you move to the left on the piano keyboard, the pitch gets lower, and as you move to the right, the pitch gets higher. The specific frequency associated with each key is determined by the mathematical relationship between the length, tension, and mass of the strings, as well as the design and construction of the piano.
It's important to note that pianos can be tuned to different reference pitches, and historical or specialized pianos may have variations in their tuning systems. However, the fundamental principle remains the same: each piano key produces a specific frequency of sound.