Storage Concerns: The Size of Sound
Ok, now we know about bits, and how to copy them from one place to another. But, where exactly do we put all these bits in the first place?
One familiar digital storage medium is the compact disk (CD). Bits are encoded on a CD as a series of pits in a metallic surface. The length of a pit corresponds to the state of the bit (on or off). As we’ve seen, it takes a lot of bits to store high-quality digital audio — a standard 74-minute CD can have more than 6 billion pits on it!
This photo shows what standard CD pits look like under high magnification. A CD stores data digitally, using long and short pits to encode a binary representation of the sound for reading by the laser mechanism of a CD player. Thanks to Evolution Audio and Video in Agoura Hills California for this photo from their A/V Newsletter (Jan 1996). The magnification is 20k.
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Physically, a CD is composed of a thin film of aluminum embedded between two discs of polycarbonate plastic. Information is recorded on the CD as a series of microscopic pits in the aluminum film arranged along a continuous spiral track. If expanded linearly, the track would span over three miles. Using a low power infrared laser (with a wavelength of 780 nm), the data is retrieved from the CD using photosensitive sensors that measure the intensity of the reflected light as the laser traverses the track. Since the recovered bit stream is simply a bit pattern, any digitally encoded information can be stored on a CD. There is no permission for this.
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Putting Everything Together
Ok, now we know about sampling rates, bit width, number systems, and a lot of other stuff. How about a nice practical example that ties it all together?
We're composers working in a digital medium. We've, like, got some cool sounds or something. We want to store them, because, as we pointed out, they're really, like, cool or something. How do we figure out how much storage we need?
Let’s assume we’re working with a stereo (two independent channels of sound) signal, and 16-bit samples. We’ll use a sampling rate of 44,100 times/second.
One 16-bit sample takes 2 bytes of storage space (remember that 8 bits = 1 byte). Since we’re in stereo, we need to double that number (there’s one sample for each channel) to 4 bytes per sample. For each second of sound we will record 44,100 four-byte stereo samples, giving us a data rate of 176.4 kilobytes (176,400 bytes) per second.
Let's review what we saw above, because we know this can get a bit complicated. There are 60 seconds in a minute, so one minute of high quality stereo digital sound takes 176.4 * 60 kB or 10.584 megabytes (10,584 KB) of storage space. In order to store 1 hour of stereo sound, at this sampling rate and resolution, we need 60 * 10.584MB, or about 600MB. This is more or less the amount of sound information on a standard commercial audio CD (actually, they can store closer to 80 minutes comfortably). One gigabyte is equal to 1,000 megabytes, so a standard CD is around two-thirds of a gigabyte.
One good rule of thumb is that CD quality sound currently requires about 10 megabytes per minute.
