Re: Why are CDs sampled at 44.1 kHz? Why not 44 kHz or 45kHz?

OneOff Media 
http://www.oneoffcd.com/info/historycd.cfm says that the decision was 
an agreement between Sony and Philips, with this timeline:

1969	Sony introduces it's 13-bit PCM digital recorder at a 47.25 kHz 
(47,250 time per second) sampling rate. The digital recording is sent to a 
2" video tape. Klass Compaan, a Dutch physicist comes up with the idea 
for the Compact Disc.

1970	At Philips, Compaan and Pete Kramer complete a glass disc 
prototype and determine that a laser will be needed to read the 
information.

1978	Philips releases the video disc player
Sony sells the PCM-1600 and PCM-1 (digital audio processors)
"Digital Audio Disc Convention" Held in Tokyo, Japan with 35 different 
manufacturers.
Philips proposes that a worldwide standard be set.

1979	Prototype CD System demonstrated in Europe and Japan.
Sony agrees to join in collaboration.
Sony & Philips compromise on the standard sampling rate of a CD -- 44.1 
kHz (44,100 samples per second)

1980	Compact Disc standard proposed by Philips & Sony.

1981	Matsushita accepts Compact Disc Standard
Digital Audio Disc Committee also accepts Compact Disc Standard.
=============
According to this website from Columbia University

http://www.cs.columbia.edu/~hgs/audio/44.1.html, the decision was 
logical giving the desire for compatibility with televisions with two 
standards consistent with 50 Hz and 60 Hz electricity:

Explanation of 44.1 kHz CD sampling rate

The CD sampling rate has to be larger than about 40 kHz to fulfill the 
Nyquist criterion that requires sampling at twice the maximum analog 
frequency, which is about 20 kHz for audio. The sampling frequency is 
chosen somewhat higher than the Nyquist rate since practical filters 
neede to prevent aliasing have a finite slope. 

Digital audio tapes (DATs) use a sampling rate of 48 kHz. It has been 
claimed that thier sampling rate differs from that of CDs to make digital 
copying from one to the other more difficult. 48 kHz is, in principle, a better 
rate since it is a multiple of the other standard sampling rates, namely 8 
and 16 kHz for telephone-quality audio. Sampling rate conversion is 
simplified if rates are integer multiples of each other. 

From John Watkinson, The Art of Digital Audio, 2nd edition, pg. 104: 


"Video recorders... were adapted to store audio samples by creating a 
pseudo-video waveform which would convey binary as black and white 
levels. The sampling rate of such a system is constrained to relate simply 
to the field rate and field structure of the television standard used, so that 
an integer number of samples can be stored on each usable TV line in 
the field. 

Such a recording can be made on a monochrome recorder, and these 
recording are made in two standards, 525 lines at 60 Hz and 625 lines at 
50 Hz. Thus it is possible to find a frequency which is a common multiple 
of the two and is also suitable for use as a sampling rate. 

The allowable sampling rates in a pseudo-video system can be deduced 
by multiplying the field rate by the number of active lines in a field 
(blanking lines cannot be used) and again by the number of samples in a 
line. By careful choice of parameters it is possible to use either 525/60 or 
625/50 video with a sampling rate of 44.1KHz. 

In 60 Hz video, there are 35 blanked lines, leaving 490 lines per frame or 
245 lines per field, so the sampling rate is given by : 

60 X 245 X 3 = 44.1 KHz 

In 50 Hz video, there are 37 lines of blanking, leaving 588 active lines per 
frame, or 294 per field, so the same sampling rate is given by 

50 X 294 X3 = 44.1 Khz. 

The sampling rate of 44.1 KHz came to be that of the Compact Disc. Even 
though CD has no video circuitry, the equipment used to make CD 
masters is video based and determines the sampling rate. 

=============
According to Wikipedia at 

http://en.wikipedia.org/wiki/Compact_disc#Origins_of_44.1_kHz_sampling:

Origins of 44.1 kHz sampling

The highest frequency that a human ear can detect is approximately 
20,000 Hz. The compact disc was designed with the capability to contain 
the full audible range, and thus overcome the limitations of previous 
consumer-level audio carriers. The provable Nyquist–Shannon sampling 
theorem states that when quantizing a signal of a given bandwidth 
(20 kHz in this case, 0 - 20 kHz), in order to be able to reproduce the 
original waveform perfectly from the digitized information, the sampling 
rate used in the quantization has to be more than twice the amount of 
bandwidth. Thus, the sample rate needed to be over 40 kHz. As real-world 
components do not adhere to the ideal situation behind the theorem, and 
CD players designed with even lower-class analogue components might 
not achieve desired results (producing audible distortion), the sampling 
rate was raised well over the ideal minimum requirement.

The exact sampling rate of 44.1 kHz is inherited from a method of 
converting digital audio into an analog video signal for storage on video 
tape, which was the most affordable way to store it at the time the CD 
specification was being developed. A device that turns an analog audio 
signal into PCM audio, which in turn is changed into an analog video 
signal is called a PCM adapter.

PCM technology could store six samples (three samples per each stereo 
channel) in a single horizontal line. A standard NTSC video signal has 
245 usable lines per field, and 59.94 fields/s, which works out at 44,056 
samples/s. Similarly PAL has 294 lines and 50 fields, which gives 44,100 
samples/s.

*	This system could either store 14-bit samples with some error 
correction, or 16-bit samples with almost no error correction.
*	There was a long debate over whether to use 14 or 16 bit samples 
and/or 44,056 or 44,100 samples/s when the Sony/Philips task force 
designed the compact disc; 16 bits and 44.1 kilo-samples/s prevailed.