I've been through the PHB and DMG and not been able to find any specific rules for this. Clearly the string instruments must be played two-handed, but I don't see why my bard couldn't be playing the pan flute or horn in one hand (as a focus for his bardic spells) and wielding a weapon or shield in his other.
3 Answers
Pan flutes vary in size, as a simple Google image search reveals. Depending on the style, it might require one or two hands. A simple 4 or 5 pipe flute is certainly designed for single hand use, while a 20 pipe flute may not be reasonable to use in a single hand. In extreme circumstances, you might even argue it occupies a shield slot.
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6\$\begingroup\$ gasp My pan flute could be incorporated into my shield! Like that battle-axe/guitar I saw. \$\endgroup\$– TempCommented May 18, 2015 at 14:55
Regarding horns, I have successfully played my trumpet with only one hand many times, and I am not a superhuman adventurer!
If you can play with no hands, you should be able to play with one hand.
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\$\begingroup\$ I've been playing with a drum and shawm around the neck of my dwarf, while wading into battle with a battleaxe. Inspired by these types of musicians. \$\endgroup\$– GMNoobCommented May 18, 2015 at 15:04