When two people play the same note on different instruments, the resulting sound waves are generally not identical. Although they may have the same fundamental frequency, there are several factors that contribute to the differences in the sound waves produced.
Tone quality: Each instrument has its unique tone quality or timbre, which is determined by the instrument's construction, materials, and playing technique. For example, a note played on a piano will have a different timbre compared to the same note played on a trumpet or a violin.
Harmonic content: Instruments produce not only the fundamental frequency but also a series of harmonics, which are multiples of the fundamental frequency. The relative strength and distribution of these harmonics vary between instruments, affecting the overall sound wave.
Attack and decay: The way a note is initiated and ended, including the attack (how quickly the sound starts) and decay (how quickly the sound fades), can differ between instruments. These variations can result in noticeable differences in the shape and duration of the sound waves.
Vibrato and articulation: Individual players may add their own expressive elements, such as vibrato (small pitch variations) or different articulation techniques, which can modify the sound wave.
Environmental factors: The acoustics of the room or performance space, as well as the microphone or recording equipment used, can introduce additional variations to the captured sound waves.
While the fundamental frequency may be the same, the combination of these factors makes the resulting sound waves distinct for each instrument. These differences contribute to the rich variety of sounds we hear in music.