What property distinguishes notes played on both a trumpet and a clarinet if they have the same pitch and loudness?

Answer 1

The property is call timbre, and different timbres are cause primarily by the inclusion of additional pitches above the note being played. All instruments, other than some special purpose electronic sound generators, cause these additional pitches, or overtones to sound.

For a somewhat overly simple explanation of overtones, if you picture a string on a guitar, the fundamental pitch is created by the string vibrating over the full length the player allows to vibrate (the length between the bridge and the fret). A wave of that length is the primary sound.

In reality, plucking a sting creates waves of all different waves lengths. Most such waves move up and down the string and quickly cancel each other out. A wave the full length of the string won't move and will be sustained. An additional wave, exactly half that length will also be sustained, as will waves exactly one third and one fourth the length of that free string length, etc. Any length of wave that fits exactly within the length of the free string will be sustained. These shorter, higher pitched waves are called over tones.

The same thing is true for waves in a column of air like one in a Trumpet or Clarinet. Different instruments allow different combinations of overtones to be prominent, and that cause the different timbres.