3.3.7 Representing Sound — AQA 8525

Analogue vs Digital Sound

Sound is a continuous analogue wave — it can take any amplitude value at any point in time. Computers can only store digital data (discrete binary values), so analogue sound must be converted.

Analogue-to-Digital Conversion (ADC)

An Analogue-to-Digital Converter (ADC) converts a continuous sound wave into a sequence of numbers by sampling: measuring the amplitude of the wave at regular intervals.

Purple line = sound wave | Green dots = samples taken | Dashed lines = sample intervals

Sample Rate

Sample rate is the number of samples taken per second, measured in Hertz (Hz) or kilohertz (kHz).

Sample rate	Quality	Common use
8,000 Hz (8 kHz)	Low	Phone calls
22,050 Hz (22.05 kHz)	Medium	AM radio quality
44,100 Hz (44.1 kHz)	High	CD audio (standard)
96,000 Hz (96 kHz)	Very high	Professional studio recordings

A higher sample rate captures more of the original waveform — the digital audio more closely matches the original. But it also means more samples to store, increasing file size.

Bit Depth (Sample Resolution)

Bit depth (also called sample resolution) is the number of bits used to store each sample's amplitude value.

Bit depth	Amplitude levels	Quality
8-bit	256 levels	Low — noticeable noise
16-bit	65,536 levels	High — CD quality
24-bit	16,777,216 levels	Studio quality

Higher bit depth = more precise amplitude values = smoother, higher quality audio. Lower bit depth causes quantisation noise (a granular hiss caused by rounding amplitude values).

Calculating Sound File Size

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

For stereo (2 channels): multiply by 2. Then ÷ 8 for bytes, ÷ 1024 for KB, etc.

-- Example: 30 seconds of CD-quality mono audio
Sample rate = 44,100 Hz
Bit depth   = 16 bits
Duration    = 30 seconds

File size = 44,100 × 16 × 30
          = 21,168,000 bits
          = 21,168,000 ÷ 8 = 2,646,000 bytes
          ≈ 2.52 MB

-- Stereo (2 channels): × 2 = 5.04 MB

Effect of Sample Rate and Bit Depth on Quality and File Size

Change	Effect on quality	Effect on file size
Increase sample rate	More accurate reproduction of high-frequency sounds	Larger
Decrease sample rate	Loss of high-frequency detail	Smaller
Increase bit depth	More amplitude levels — less quantisation noise	Larger
Decrease bit depth	Fewer levels — more noise	Smaller

Exam tip: The formula is sample rate × bit depth × duration. Don't forget to multiply by the number of channels (1 for mono, 2 for stereo) if the question specifies. Always state units — bits first, then convert.

⚠️ Common Mistakes

Confusing sample rate (Hz) with bit depth (bits per sample) — sample rate is how often, bit depth is how precisely
Forgetting to multiply by 2 for stereo audio
Dividing by 1000 instead of 1024 when converting to KB/MB
Thinking higher sample rate always makes a better file — the quality gain depends on the original source too

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Key points

Sound is analogue; must be sampled to become digital
Sample rate = samples per second (Hz); CD = 44,100 Hz
Bit depth = bits per sample; 16-bit = 65,536 amplitude levels (CD quality)
File size (bits) = sample rate × bit depth × duration; ×2 for stereo
Higher sample rate/bit depth = better quality but larger file

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Worksheet — 3.3.7 Representing Sound

8 questions · 21 marks

Q1What is meant by 'sampling' in the context of sound digitisation?[2]

✅ Mark scheme

Mark scheme

Measuring the amplitude of the sound wave [1] at regular time intervals [1].

Q2Define 'sample rate' and state its unit of measurement.[2]

✅ Mark scheme

Mark scheme

Sample rate = the number of samples taken per second [1]; measured in Hertz (Hz) or kilohertz (kHz) [1].

Q3A mono audio file is recorded at 22,050 Hz sample rate, 8-bit depth, for 10 seconds. Calculate its file size in bytes.[3]

✅ Mark scheme

Mark scheme

22,050 × 8 × 10 = 1,764,000 bits [1]; ÷ 8 = 220,500 bytes [1] (≈215 KB [1 bonus]).

Q4Explain the difference between sample rate and bit depth.[2]

✅ Mark scheme

Mark scheme

Sample rate is how often measurements are taken per second (frequency of sampling) [1]; bit depth is how many bits are used to represent each sample's amplitude (precision of each sample) [1].

Q5Calculate the file size in MB for a stereo audio recording at 44,100 Hz, 16-bit, for 3 minutes. (1 MB = 1024 × 1024 bytes)[4]

✅ Mark scheme

Mark scheme

Duration = 180 seconds [1]; 44,100 × 16 × 180 × 2 (stereo) = 254,016,000 bits [1]; ÷ 8 = 31,752,000 bytes [1]; ÷ (1024×1024) ≈ 30.3 MB [1].

Q6What is quantisation noise and what causes it?[2]

✅ Mark scheme

Mark scheme

Quantisation noise is unwanted noise/hiss in digital audio [1]; caused by rounding amplitude values to the nearest available level when bit depth is too low [1].

Q7A musician wants to reduce the file size of a recording without changing its duration. Give two ways to do this, and describe the trade-off for each.[4]

✅ Mark scheme

Mark scheme

Reduce sample rate [1] — loss of high-frequency detail, sound less accurate [1]; reduce bit depth [1] — fewer amplitude levels, more quantisation noise [1].

Q8CD audio uses a sample rate of 44,100 Hz. Human hearing goes up to about 20,000 Hz. Explain why 44,100 Hz is sufficient to reproduce all sounds humans can hear.[2]

✅ Mark scheme

Mark scheme

To accurately reproduce a frequency, the sample rate must be at least twice that frequency (Nyquist theorem) [1]; 2 × 20,000 = 40,000 Hz, and 44,100 > 40,000, so all humanly-audible frequencies are captured [1].

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Analogue vs Digital Sound

Analogue-to-Digital Conversion (ADC)

Sample Rate

Bit Depth (Sample Resolution)

Calculating Sound File Size

Effect of Sample Rate and Bit Depth on Quality and File Size

Key points

Worksheet — 3.3.7 Representing Sound

Mini Test — 3.3.7 Representing Sound