What makes a violin sound like a violin and not a trumpet, even though they are both sounding a note in the same pitch?
The answer is harmonic content.
A pure tone of a single frequency is essentially a sinusoidal vibration... repeated displacement back and forth which, if plotted against time, will appear as a "sine wave". When you drop a stone into water, and waves ripple out, the pattern of wave crest and trough is a reasonable approximation.
When a violin sounds a note, it is not producing a pure (sinusoidal) tone. Neither is any other musical instrument. There is a "fundamental", which is a pure sine wave at the frequency corresponding to the "pitch" of the note, accompanied by a set of "overtones" of other frequencies. These overtones occur at frequencies which are specific whole number multiples of the fundamental. The presence of an overtone at a given frequency, and its relative amplitude creates the harmonic structure of a given sound, and creates the sound you recognize as a violin vs a trumpet, or whatever.