📄 Paper 2 · 4.5 Data Representation
4.5.6b Representing Sound
AQA 7517 · A-Level Computer Science · ~13 min read

Analogue vs Digital Sound

Sound is naturally an analogue (continuous) signal — a pressure wave in air. Computers store digital (discrete) values, so sound must be sampled (digitised) at regular intervals.

Analogue-to-Digital Conversion (ADC)

A microphone converts sound waves to an electrical signal. The ADC then samples this signal at fixed time intervals, measuring the amplitude at each moment. Each measurement is stored as a binary number. On playback, a DAC (Digital-to-Analogue Converter) reconstructs the wave.

Key Properties of Digital Audio

PropertyDefinitionEffect of increasing
Sample rateNumber of samples taken per second (Hz)Better frequency reproduction, larger file
Bit depthNumber of bits per sample (resolution of each measurement)Better dynamic range/amplitude accuracy, larger file
ChannelsMono (1) or stereo (2) or surroundMore channels = larger file

Nyquist Theorem

To accurately reproduce a sound of frequency f, the sample rate must be at least 2f. CD audio uses 44,100 Hz (44.1 kHz) — capable of capturing up to 22,050 Hz (above the human hearing range of ~20 kHz). If the sample rate is too low, high-frequency sounds are lost or distorted.

Calculating Audio File Size

Formula: File size (bits) = sample rate × bit depth × channels × duration (seconds)

Worked example

Stereo audio, 44,100 Hz sample rate, 16-bit depth, 3 minutes:

  • 3 min = 180 seconds
  • Bits = 44,100 × 16 × 2 × 180 = 254,016,000 bits
  • Bytes = 254,016,000 ÷ 8 = 31,752,000 bytes ≈ 31.75 MB

Common Audio Formats

FormatCompressionUse case
WAVNone (lossless)High quality, large files, professional audio
AIFFNone (lossless)Apple equivalent of WAV
MP3LossyMusic streaming, reduced file size
FLACLosslessArchival, audiophile quality

Quality vs File Size Trade-off

Higher sample rate and bit depth produce better audio quality but larger files. Compression (MP3) reduces file size by discarding inaudible frequencies (psychoacoustics) but introduces quality loss. This is the key trade-off: quality vs storage/bandwidth efficiency.

Exam tip: Know the formula: file size = sample rate × bit depth × channels × duration (÷ 8 for bytes). Understand that CD quality is 44,100 Hz, 16-bit, stereo. Know that higher sample rate AND higher bit depth both improve quality AND increase file size. The Nyquist theorem requires sample rate ≥ 2 × max frequency. AQA asks calculation questions regularly — practise showing working.
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Worksheet — 4.5.6b Representing Sound

8 questions · instantly marked · AQA 7517 standard

Q1Explain the terms 'sample rate' and 'bit depth' in the context of digital audio.[4]
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Sample rate: the number of amplitude measurements (samples) taken per second from the analogue signal [1]; higher sample rate = more accurate frequency reproduction [1]; bit depth: the number of bits used to represent each sample's amplitude value [1]; higher bit depth = greater dynamic range / more accurate amplitude representation [1].
Q2Calculate the uncompressed file size in MB of 5 minutes of stereo audio at 44,100 Hz sample rate and 16-bit depth. Show all working.[4]
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Duration = 5 × 60 = 300 seconds [1]; total bits = 44,100 × 16 × 2 × 300 = 423,360,000 bits [1]; ÷ 8 = 52,920,000 bytes [1]; ÷ 1,000,000 ≈ 52.92 MB [1].
Q3State the Nyquist theorem and explain why CD audio uses a sample rate of 44,100 Hz.[3]
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Nyquist theorem: to accurately reproduce a sound of frequency f, the sample rate must be at least 2f [1]; human hearing range is approximately 20 Hz to 20,000 Hz [1]; 44,100 Hz > 2 × 20,000 Hz = 40,000 Hz, so CD audio can capture the full range of human hearing with margin [1].
Q4Describe what happens during analogue-to-digital conversion of a sound wave.[3]
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A microphone converts the sound pressure wave to an analogue electrical signal [1]; the ADC samples the amplitude of this signal at regular intervals (determined by the sample rate) [1]; each sample's amplitude is stored as a binary number (the precision determined by the bit depth) [1].
Q5A recording is taken at 22,050 Hz sample rate, 8-bit depth, mono, for 1 minute. Calculate the file size in kilobytes.[3]
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Bits = 22,050 × 8 × 1 × 60 = 10,584,000 bits [1]; ÷ 8 = 1,323,000 bytes [1]; ÷ 1,000 = 1,323 KB [1].
Q6Explain why increasing the sample rate improves audio quality but also increases file size.[2]
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More samples per second capture more detail in the sound wave's frequency content [1]; more samples means more data is stored, so the file is larger [1].
Q7Compare WAV and MP3 formats in terms of quality and file size.[2]
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WAV is uncompressed — lossless, maintains original audio quality but produces large files [1]; MP3 uses lossy compression — discards inaudible frequencies, producing much smaller files at the cost of some audio quality [1].
Q8A developer records a 30-second stereo podcast at 48,000 Hz and 24-bit depth. Calculate the uncompressed size in MB and suggest why compression would be appropriate here.[4]
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Bits = 48,000 × 24 × 2 × 30 = 69,120,000 bits [1]; ÷ 8 = 8,640,000 bytes = 8.64 MB [1]; compression is appropriate: podcast speech quality doesn't require 24-bit depth [1]; compression reduces file size significantly for streaming/download without perceptible quality loss for speech [1].
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Mini Test — Representing Sound

10 questions · 10 minutes

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