These overtones are what give each musical instrument its unique timbre or tone color. For example, a piano and a guitar may play the same note at the same pitch, but they will sound different due to the different overtones that are present.
The number and relative strengths of the overtones present in a sound are determined by the shape, size, and material of the vibrating object. For example, a stringed instrument like a guitar or violin will have a different set of overtones than a wind instrument like a flute or clarinet.
The study of overtones is called harmonics. Harmonics play an important role in music theory, composition, and performance.