How do you account for the fact that two strings can be used to give notes of the same pitch and loudness but of different quality?

(N/A) The 'quality' or 'timbre' of a sound is determined by the presence and relative intensity of overtones or harmonics.
Even if two strings produce notes of the same fundamental frequency (pitch) and amplitude (loudness),they may vibrate in different modes or have different harmonic structures depending on the material,tension,and point of plucking.
These additional harmonics superimpose on the fundamental frequency,creating a unique waveform for each string.
Therefore,the overall effect of these harmonics results in a different 'quality' of sound for each string.