Why does a smaller string on an instrument make a higher note?

Question

Why does a smaller string on an instrument make a higher note?

Answer 1

Because it vibrates at a higher frequency (faster).

Answer 2

The string oscillates in a wave.  That wave has a length, which is the length of the string (or is at least a function of it).

By definition, the length of a wave is inversely proportional to its frequency:  (wavelength = constant / frequency, or frequency = constant / wavelength).  [The constant is usually something like the speed of the wave in medium, but not always].

Thus, a shorter wave produces a higher frequency, and higher frequency SOUND waves have higher pitch, or note.

Answer 3

because it makes a higher altitude