Final answer:
The vibration of a musical instrument is influenced by its size, shape, and proportion; the material it is made of; and how the vibration is produced, with all factors affecting the sound's properties.
Step-by-step explanation:
The factors that influence the vibration of an instrument include: 1) Size, shape, and proportion of the instrument, 2) Material from which it is made, and 3) How the vibration is produced. All these factors contribute to the production and quality of sound from an instrument. For example, the size of a musical instrument affects the frequency and wavelength of the sound it produces; smaller instruments like a tambourine produce higher frequency, shorter wavelength sounds, while larger instruments like a drum emit lower frequency, longer wavelength sounds. Additionally, the material contributes to how sound waves are transmitted and the quality of the sound, with different materials affecting the instrument's resonance and tone. The mechanism of sound production, such as plucking a string or blowing into a tube, plays a role in shaping the characteristics of the sound wave, including its reinforcement through resonance.