It's complicated, because most instruments cover a wide range when you factor in harmonics. Bass instruments indeed have root tones around the lower end, say 20-160hz (hz defined as how many vibrations per second you're dealing with, at 20 hz picture a string wobbling back and forth at the rate). Each doubling of frequency equals one octave, so 20-160 would represent about 3 octaves. Root tones aren't all you need to worry about though, because the sound you hear could have lots of higher frequencies factored in. For example, on a standup acoustic bass you could hear the snap of the strings or a finger sliding along a string at a higher frequency. The only pure tone you'll hear in audio is a cheesy old synthesizer playing a sine wav. Unless you're into early Moog music you won't be hearing that often. A sine wav is defined as a pure tone, at one frequency, with no harmonics. Harmonics usually exist at one octave above your root tone, 2 octaves above, an octave and a fifth above, etc.
Every instrument has its own set of harmonics that it will trigger. The easiest example is on a piano, when you strike one key it strikes the strings for that note. The motion of those strings and of the entire mechanism can allow other strings to vibrate. There are felt pads that rest on the strings to cut off the harmonic resonance but you can lift those by using the sustain pedal. On a piano, when you hold the sustain pedal you're unlocking a huge amount of harmonic information, which makes the instrument sound very full, and triggers frequencies across a wide range.
So, for a quick reference, bass is indeed produced by the obvious stringed bass instruments, plus many other instruments including the piano, tuba, cello.... The midrange covers most orchestra instruments, voices, the list is endless in that kind of range. Remember that each doubling of frequency represents an octave. On a piano the middle A is 440hz, double that a few times you're up to the top of the piano at 3520hz. Beyond that you're really going to lose the ability to distinguish individual musical notes, and it turns to harmonic detail. We identify almost every instrument in the world by their harmonic details, not by their root tones, so don't think that 4000-20000 hz is useless. Getting that part right is what Hi-fi is all about.
Hope that helps. Lot of terms in there but I tried to define as much as possible. Feel free to ask for clarification on any of that.
