Why does each musical instrument sound different?
Instruments sound different because the relative strength (loudness) of their harmonics are different.
The relative loudness of the overtones depends on the materials, size, and shape of the instrument as well as the technique of the person playing it. Some overtones may not even have any loudness at all. The relative strengths of the harmonics also change vibrations decay and resonate with each other over time.
Each instrument has a unique harmonic signature based on its unique combination of overtones. Our brains perceive these harmonics in way that allows us to recognize the “voice” of the instrument (and human voices, too!). This perception is called timbre.
Such impressions may be described using adjectives such as warm, mellow, bright, velvety, nasal, brassy, tinny, tender, and countless others.
Furthermore, because their harmonic signatures can be different, even similar instruments can sound different. A spinet piano, for example, sounds quite different from a grand piano. Even grand pianos sound different from each other. In fact, two pianos that are the exact same model may not sound exactly alike.