Yes but as several have commented, a sampling rate of 44.1 or 48 WILL reproduce all audible frequencies, (unless you're a dog), accurately.
When it comes to high resolution audio formats, (SACD or DVD audio), the bit depth plays a far more important role in producing the high quality audio than does the sample rate. 16 bit audio can only produce roughly 65,000 levels between noise floor and clipping; 24 bit audio can produce around 2.5 million levels. This is particularly important with classical music which is almost never at full amplitude, and, hence, almost never using all 16 bits on a CD. Any musical instrument produces a string of harmonics which are progressively lower level as their frequency increases; thus on a regular CD, the highest frequency harmonics, which represent the most complex component of the entire audio signal, although still well within the frequency range of CDs, are at such a low level that they are only read very poorly using a couple of bits. However when these audio signals are recorded using DSD or 24bit or higher bit depth, this harmonic content is
far more accurately reproduced, giving the impression of an enhanced high frequency content, no matter where your personal hf cutoff point is, (I think mine is somewhere between 14k and 15k).
> From: Mark Durenberger <[log in to unmask]>
>To: [log in to unmask]
>Sent: Friday, August 17, 2012 11:42:07 AM
>Subject: Re: [ARSCLIST] Bit rates over 48 kHz
>Best explanation I've seen for doing this!
>-----Original Message----- From: Toby Seay
>Yes, 44.1KHz and 48KHz cover the entire hearing spectrum. However, it does
>not cover it well. Resolution gets worse as you go higher in the frequency
>spectrum. Therefore, really high frequencies only get sampled a few times.
>For instance, a 44.1KHz sample rate is only capable of sampling a 12KHz
>frequency 3.675 times a second. That leaves you with a very poor
>digitization at 12KHz. 96KHz does a much better job at providing a digital
>representation of higher frequencies.