1.2.4g Representing Sound — OCR J277

Analogue vs Digital Sound

Sound is a continuous analogue wave — it varies smoothly over time with infinitely many possible values. Computers can only store discrete digital values, so sound must be converted. This process is called sampling.

A microphone converts sound pressure waves into an analogue electrical signal
An ADC (Analogue-to-Digital Converter) samples the analogue signal at regular intervals and converts each sample to a binary number
On playback, a DAC (Digital-to-Analogue Converter) reconstructs the analogue signal from the stored binary values

Sampling Rate

The sampling rate (also called sample rate or sampling frequency) is the number of samples taken per second. It is measured in Hertz (Hz) or kilohertz (kHz).

Sampling rate	Quality level	Typical use
8,000 Hz (8 kHz)	Low quality	Telephone voice
22,050 Hz (22 kHz)	Medium quality	AM radio quality
44,100 Hz (44.1 kHz)	High quality	CD audio standard
48,000 Hz (48 kHz)	Professional	DVD / professional audio

Higher sampling rate → more samples per second → the digital waveform more closely matches the original analogue signal → better sound quality → larger file size.

The Nyquist theorem states that the sampling rate must be at least twice the highest frequency you want to capture. Human hearing goes up to ~20 kHz, so CD audio uses 44,100 Hz (more than 2 × 20,000).

Bit Depth

Bit depth (also called sample resolution or sample size) is the number of bits used to store each individual audio sample. More bits = more possible amplitude values = more accurate representation of the analogue waveform.

Bit depth	Amplitude levels	Use
8-bit	256 levels	Old gaming, voice, low quality
16-bit	65,536 levels	CD audio standard
24-bit	16,777,216 levels	Professional studio recording

Number of amplitude levels = 2^(bit depth). Higher bit depth reduces quantisation error — the difference between the actual analogue value and the stored digital approximation.

Calculating File Size of Audio

The uncompressed file size of a digital audio recording is:

File size (bits) = Sample rate × Bit depth × Duration (seconds)

For stereo (2 channels), multiply by 2. Then divide by 8 for bytes.

Worked Example 1

30-second mono recording at 44,100 Hz, 16-bit:

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

Worked Example 2 — Stereo

60-second stereo recording at 44,100 Hz, 16-bit:

44,100 × 16 × 60 × 2 = 84,672,000 bits
÷ 8 = 10,584,000 bytes ≈ 10.09 MB

Effect on File Size and Quality

Factor	Increasing causes	Effect on quality
Sampling rate	Larger file size	Better frequency reproduction, clearer high sounds
Bit depth	Larger file size	More amplitude levels, less noise, greater dynamic range
Duration	Larger file size	No effect on quality — just more data
Channels (mono→stereo)	Doubles file size	Spatial audio / stereo effect

Exam tip: File size formula for sound: sample rate × bit depth × duration (÷ 8 for bytes, ×2 for stereo). You will almost certainly be given values and asked to calculate. Also be ready to explain the effect of increasing sample rate or bit depth on quality and file size — two separate marks, so give two separate points.

⚠️ Common Mistakes

Confusing sampling rate (samples/second) with bit depth (bits/sample) — they are different things
Forgetting to ×2 for stereo when the question specifies stereo audio
Forgetting to divide by 8 to convert bits to bytes
Saying higher sample rate = "more samples per sample" — it means more samples per SECOND
Mixing up Hz and kHz — 44.1 kHz = 44,100 Hz, not 44.1

✅ Notes completed!

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What's in this video

• Analogue vs digital sound and why we need sampling
• Sampling rate (Hz): what it means, higher = better quality + larger file
• Bit depth: amplitude levels, quantisation error
• File size formula: sample rate × bit depth × duration ÷ 8

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Worksheet — 1.2.4g Representing Sound

8 questions · 20 marks · Show all calculations

Q1What is sampling? Why is it needed to represent sound digitally?[2]

✅ Mark scheme

Sampling is measuring the amplitude (volume) of an analogue sound wave at regular time intervals [1]; it is needed because computers can only store discrete digital values, not continuous analogue signals [1].

Q2What is sampling rate and what unit is it measured in?[2]

✅ Mark scheme

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

Q3What is bit depth and how does it affect audio quality?[2]

✅ Mark scheme

Bit depth is the number of bits used to store each audio sample [1]; higher bit depth = more amplitude levels = more accurate representation of the original sound / less quantisation error [1].

Q4Calculate the file size in bytes of a 10-second mono audio clip sampled at 44,100 Hz with 16-bit depth.[3]

✅ Mark scheme

44,100 × 16 × 10 = 7,056,000 bits [1]; ÷ 8 = 882,000 bytes [1]; method/formula correct [1].

Q5A stereo audio file is recorded at 48,000 Hz, 24-bit depth, for 60 seconds. Calculate the file size in MB (1 MB = 1,048,576 bytes). Show all working.[4]

✅ Mark scheme

48,000 × 24 × 60 × 2 = 138,240,000 bits [1]; ÷ 8 = 17,280,000 bytes [1]; ÷ 1,048,576 ≈ 16.48 MB [1]; ×2 for stereo included [1].

Q6How many amplitude levels can be represented by 8-bit depth? Show your working.[2]

✅ Mark scheme

2⁸ = 256 amplitude levels [1+1 for showing working].

Q7Explain why increasing the sampling rate increases the quality of a digital audio recording. State one disadvantage.[3]

✅ Mark scheme

More samples taken per second → digital waveform captures more detail of the original analogue signal → more accurate reproduction → higher quality sound [2]; disadvantage: larger file size / requires more storage space [1].

Q8Describe what quantisation error is. How can it be reduced?[2]

✅ Mark scheme

Quantisation error is the difference between the actual analogue amplitude value and the nearest stored digital value [1]; it can be reduced by increasing the bit depth (more levels available, so the nearest digital value is closer to the actual value) [1].

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Analogue vs Digital Sound

Sampling Rate

Bit Depth

Calculating File Size of Audio

Worked Example 1

Worked Example 2 — Stereo

Effect on File Size and Quality

What's in this video

Worksheet — 1.2.4g Representing Sound

Mini Test — 1.2.4g Representing Sound