Question

Why musical instruments show variation on displays with different pitch of sound?

Answer 1

Most instruments produce not only the fundamental note like a440 but a whole series of tones in an integer relationship, called Overtones i.e. 1*440, 2*440, 3*440 etc. the difference between a piano note and a guitar note is the relative loudness or amplitude of each overtone. This is part of what defines the difference between one instrument and another. Another part is the Envelope - the change in amplitude over time of the sound, a piano has a very sharp beginning or "attack" and a violin has a relatively slow attack. 

Also the amplitude of each overtone has it's own envelope which is different for each instrument. 

Together these things  make a unique sound or Timbre that makes one instrument different from another.