People's ear can hear sound whose frequencies range from 20 Hz to 20 kHz. Based on the Nyquist theorem, recording rate should be at least 40 kHz, is it the reason choosing 44.1 kHz?
it is true that, like any convention, the choice of 44.1 kHz is sorta an historical accident. there are a few other historical reasons.
of course, the sampling rate must exceed 40 kHz if you want high quality audio with a bandwidth of 20 kHz.
there was discussion of making it 48.0 kHz (it was nicely congruent with 24 frame/second films and the ostensible 30 frames/second in North American TV), but given the physical size of 120 mm, there was a limit to how much data the CD could hold, and given that an error detection and correction scheme was needed and that requires some redundancy in data, the amount of logical data the CD could store (about 700 MB) is about half of the amount of physical data. given all of that, at the rate of 48 kHz, we were told that it could not hold all of Beethoven's 9th but that it could hold the entire 9th on one disc at a slightly slower rate. so 48 kHz is out.
still, why 44.1 and not 44.0 or 45.0 kHz or some nice round number?
then at the time, there existed a product in the late 70s called the Sony F1 that was designed to record digital audio onto readily-available video tape (Betamax not VHS). that was at 44.1 kHz (or more precisely 44.056 kHz). so this would make it easy to transfer recordings, without resampling and interpolation, from the F1 to CD or in the other direction.
my understanding of how it gets there is that the horizontal scan rate of NTSC TV was 15.750 kHz and 44.1 kHz is exactly 2.8 times that. i'm not entirely sure by i believe what that means is that you can have 3 stereo sample pairs per horizontal line, and for every 5 lines, where you would normally have 15 samples, there are 14 samples plus one additional sample for some parity check or redundancy in the F1. 14 samples for 5 lines is the same as 2.8 samples per horizontal line and with 15750 lines per second, that comes out to be 44100 samples per second.
now, since color TV was introduced, they had to bump down slightly the horizontal line rate to 15734 lines per second. that adjustment leads to the 44056 samples per second in the Sony F1.
Look http://www1.cs.columbia.edu/~hgs/audio/44.1.html for example. You should use sampling rate more than 40 kHz because of anti-aliasing filters. You should have some reserve in frequency to prevent signal distortion due to filter's reponse slope. The actual value of 44.1 kHz was suggested by Sony corp when audio recording standard was under discussion in 1979. They used this rate widely for that moment.
So it's generally historical reason.
Look [http://batmobile.blogs.ilrt.org/audio-analysis-on-an-iphone for description . .A theorem called the Nyquist sampling theorem states that in order to sample a signal of X Hz without significant loss of quality, you need to sample at 2X the frequency. The limit of human hearing is approximately 20kHz, which hence requires a sample rate of approximately 40Khz. This is why CDs are sampled at 44Khz. i.e. each second of recording in a CD contains 44,000 measurements of the highest possible frequency contained in the recording.