Physics
Physics
Problem
Explain why only certain discrete frequencies (and not a continuous range) are produced when a string is set into vibration with both ends fixed.Intuitive explanation
When a string vibrates with both ends held fixed, those boundary points act as nodes—places that cannot move. This constraint means only waves that "fit" perfectly on the string, with nodes at both ends, can persist; all other patterns destructively interfere and vanish. The key insight is that the string length must equal an integer number of half-wavelengths, which directly locks the allowed wavelengths, and therefore frequencies, into a discrete set called harmonics or normal modes. This is why you hear specific pitches rather than a blur of sound.
Intuitive explanation
When a string vibrates with both ends held fixed, those boundary points act as nodes—places that cannot move. This constraint means only waves that "fit" perfectly on the string, with nodes at both ends, can persist; all other patterns destructively interfere and vanish. The key insight is that the string length must equal an integer number of half-wavelengths, which directly locks the allowed wavelengths, and therefore frequencies, into a discrete set called harmonics or normal modes. This is why you hear specific pitches rather than a blur of sound.