From the Boston Acoustics Blog Archives (circa 2011, updated 2013)
If you pick up an acoustic guitar (depending on the design of the neck) and play the top E-string on the top fret, you are playing B, at about 988 Hz. Some electrics even go a couple notes higher. A quick look at speaker specs will show a transition to the littlest driver, the tweeter, somewhere around 2,500 to 3,500 Hz, and the tweeter specializes in the highest frequency range, up to 20,000 Hz or higher.
Of course you would point out that a piccolo goes even higher than the guitar. How high? The top note on a typical piccolo is a C at 4,186 Hz, but that doesn’t explain the need for more range.
As a rule all musical instruments convey the fundamental tone AND harmonics of the tone. So if you play that 4,186 Hz C, you are also getting multiples of that frequency, at 8,372 and 12,558 and 16,744, etc. And there is the air noise (a mix of frequencies) from the person blowing into the instrument. Even the guitar’s top note of 988 Hz has plenty of harmonic content and even more if it is a steel string or electric. If you don’t convey these harmonics, you have “harmonic distortion” – and the real effect is a loss of airiness, openness, and clarity in the sound. Cover a speaker’s tweeter with your hand (avoid touching it) and you will see how dull the sound becomes. So is this top range important? Absolutely!
© Copyright 2013 Stephen Shenefield
Vaetr Design 
Most musical instruments also radiate transient frequencies generated by such acts as plucking or hammering on a string (guitar or piano), or strumming (violin). Although these frequencies die out reasonably quickly, they still add to the the overall timbre of the instrument. The transient frequencies are generally much higher than the fundamental tone of the actual note being played.
So what is the upper frequency recommended for a full range driver used with guitar? Would 12000hz capture most of the harmonics? 15000Hz? I seem to remember most guys loose the ability to hear much above 16000hz in their 40s.
Yes! 12 kHz captures most of the harmonics, and guitar amp/speaker response generally doesn’t just drop off like a rock above any specific frequency but rather tapers off more gently. When a guitar speaker has a response to 12 kHz, it is still reproducing sound at 16 kHz, just a few dB lower.