Final answer:
The bit rate for uncompressed audio CDs is 1,411.2 kbps, and an hour's worth of music would require approximately 605.2 MB of storage.
Step-by-step explanation:
Calculating Bit Rate and Storage Needs for Audio CDs
To answer the student's question about audio CDs encoding music at 44,000 Hz using 16-bit samples:
- (a) The bit rate for uncompressed music is calculated by multiplying the sample rate by the number of bits per sample. Since an audio CD uses stereo sound, we must also consider two channels (left and right). Therefore, the bit rate is 44,000 samples/second × 16 bits/sample × 2 (for stereo) = 1,411,200 bits per second or 1,411.2 kbps (kilobits per second).
- (b) To determine the number of bytes needed for an hour’s worth of music, we first multiply the bit rate by the number of seconds in an hour (3,600 seconds). The result is then divided by 8 to convert bits to bytes: 1,411,200 bits/second × 3,600 seconds/hour ÷ 8 bits/byte = 635,040,000 bytes or approximately 605.2 megabytes (MB).
An audio CD's large information-storage capacity allows for storing not just music but other forms of data, including encyclopedias, due to the precision of the digital encoding of information via pits and bumps on the disc.