For example, the fundamental frequency of a guitar string is the lowest note that the string can produce. The overtones are the higher notes that are produced when the string vibrates at multiples of the fundamental frequency. The relative strengths of the overtones depend on the tension of the string, the thickness of the string, and the way the string is plucked.
The fundamental frequency of a trumpet is also the lowest note that the trumpet can produce. However, the overtones of a trumpet are different from the overtones of a guitar string. The relative strengths of the overtones depend on the shape of the trumpet, the length of the trumpet, and the way the trumpet is played.
This is why a guitar and trumpet sound different when they play the same note. The different overtones present in the sound give each instrument its own unique timbre.