Why the piano and violin sound different when they're playing the same note? My teacher said because the amplitudes are different. Is it correct?

Your teacher is partially correct when they mention that the amplitudes are different, but this is not the primary reason why a piano and a violin sound different when playing the same note. The main reasons for the difference in sound are:

1. Method of Sound Production:

   • Piano: Sound is produced by hammers striking strings, which creates a percussive attack and a richer, fuller sound due to the multiple strings per note13.
   • Violin: Sound is produced by drawing a bow across the strings or plucking them, resulting in a smoother, more continuous sound13.

2. Harmonic Overtones and Envelope:

   • Each instrument produces unique harmonic overtones when a note is played. These overtones are additional frequencies that accompany the fundamental frequency, and their relative amplitudes (loudness) vary between instruments23.
   • The envelope refers to the attack, decay, sustain, and release (ADSR) characteristics of a sound. Different instruments have distinct envelopes, affecting how the sound begins and ends2.

3. Instrument Construction:

   • The size, shape, and material of the instruments influence how sound is projected and perceived. For example, a piano's large soundboard and body produce a more resonant sound compared to the violin's smaller soundbox13.

4. Timbre:

   • Timbre is the unique "tone color" or quality of sound that distinguishes one instrument from another. It is influenced by the instrument's design and how sound is produced23.

While amplitude (loudness) can vary between instruments, it is not the primary reason for their distinct sounds. The differences in sound production methods, harmonic overtones, envelopes, and construction all contribute to the unique timbre of each instrument.