Cambridge IGCSE Computer Science (0478) · lesson 7 of 35 · 25 min
Analogue vs Digital Sound
Sound is a continuous (analogue) wave — air pressure varying smoothly over time. Computers can only store discrete (digital) values, so we must sample the analogue wave at regular intervals and store each sample as a binary number.
This process is called Analogue-to-Digital Conversion (ADC). The reverse — converting stored digital values back to sound — is Digital-to-Analogue Conversion (DAC), performed by your speakers or headphones.
Sampling Rate and Bit Depth
CD quality audio: 44,100 Hz sampling rate, 16-bit depth, stereo (2 channels).
Nyquist theorem: To accurately reproduce a sound, the sampling rate must be at least twice the highest frequency in the sound. Human hearing tops out at ~20,000 Hz, so 44,100 Hz is sufficient.
Calculating Audio File Size
File size (bits) = sampling rate × bit depth × channels × duration (seconds)
Worked Example
Calculate the size of 3 minutes of CD-quality stereo audio
Sampling rate = 44,100 Hz, bit depth = 16, channels = 2, duration = 180 s
Bits = 44,100 × 16 × 2 × 180 = 254,016,000 bits
Bytes = 254,016,000 ÷ 8 = 31,752,000 bytes
≈ 30.3 MB uncompressed
(MP3 compression reduces this to ~3–4 MB)
What is the sampling rate of CD-quality audio?
- 22,050 Hz
- 44,100 Hz
- 48,000 Hz
- 96,000 Hz
Answer: 44,100 Hz
CD standard is 44,100 samples per second.
Increasing bit depth from 8 to 16 will:
- Double the sampling rate
- Double the file size
- Halve the file size
- Have no effect on quality
- Answer: 1
File size is proportional to bit depth; 16-bit uses twice the storage of 8-bit. According to the Nyquist theorem, to record sound up to 20,000 Hz you need a sampling rate of at least:
- 10,000 Hz
- 20,000 Hz
- 40,000 Hz
- 80,000 Hz
- Answer: 2
Nyquist: sampling rate ≥ 2 × maximum frequency = 40,000 Hz.
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