Your journey through Sound Representation
Analogue to digital, sampling rate, sampling resolution, and the file-size formula. Seven stages from theory to mastery. Click any stage card to dive in — or continue where you left off.
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Sound Representation Lab — sampling the wave
How analogue sound becomes binary: sample rate, sample resolution, and how each affects sound quality and file size.
What is Topic 1.3C?
Real-world sound is analogue — a continuous wave of pressure changes. Computers store binary — discrete numbers. To bridge the gap, we take rapid samples of the wave and store each sample as a binary number.
Two independent parameters control how faithful the digital recording is: sampling rate (how OFTEN we sample) and sampling resolution (how PRECISELY we measure each sample). Cambridge test both, especially the trap of confusing them.
Note: text is covered in 1.3A Text Representation Lab and images in 1.3B Image Representation Lab. This lesson (1.3C) covers sound only.
By the end of 1.3C you can…
- Explain that sound is analogue and must be converted to digital for storage
- Define sampling as taking measurements of the sound wave at regular intervals
- Define sampling rate as the number of samples taken per second (measured in Hz or kHz)
- Define sampling resolution (bit depth) as the number of bits used per sample
- Explain how higher sampling rate improves accuracy: more samples per second → more accurate representation of the waveform
- Explain how higher sampling resolution improves accuracy: more bits per sample → wider range of amplitudes can be recorded
- State the file size formula: sampling rate × sampling resolution × duration
- State the trade-off: higher rate or resolution improves quality but increases file size
Cambridge-approved terms
| Term | Definition |
|---|---|
| Analogue | A continuous signal, such as a real-world sound wave. |
| Digital | A signal represented using discrete numeric values (binary). |
| Sample | A measurement of the amplitude of the sound wave at a specific instant. |
| Sampling | The process of taking regular measurements of the sound wave. |
| Sampling rate | The number of samples taken per second. Measured in Hz (or kHz). |
| Sampling resolution | The number of bits used for each sample. Also called bit depth or sample depth. |
| Amplitude | The strength (height) of the sound wave at a given moment. |
| File size (bits) | sampling rate × sampling resolution × duration (in seconds). |
The three tables you must know cold
Rate vs Resolution — the two axes
| Parameter | Measured in | Effect if increased |
|---|---|---|
| Sampling rate | Hz (samples per second) | More points on the waveform → shape captured more accurately → larger file |
| Sampling resolution | Bits per sample | Wider range of amplitudes distinguishable → quieter/louder sounds captured → larger file |
These are independent — you can have high rate with low resolution, or vice versa.
Common values
| Application | Sampling rate | Sampling resolution |
|---|---|---|
| Phone (voice) | 8 kHz | 8-bit |
| CD audio | 44.1 kHz | 16-bit |
| DVD / video | 48 kHz | 16-bit or 24-bit |
| Studio | 96 kHz | 24-bit |
File size formula
| Quantity | Formula |
|---|---|
| File size in bits | sampling rate × sampling resolution × duration (seconds) |
| File size in bytes | (rate × resolution × duration) ÷ 8 |
Watch each calculation done step by step
Worked example 1 · One minute of CD-quality audio
Calculate the file size of a 60-second CD-quality mono recording (44.1 kHz, 16-bit).
Worked example 2 · Effect of doubling sampling rate
An audio file uses 22.05 kHz sampling rate. If the rate is doubled to 44.1 kHz (with all else unchanged), what happens to the file size?
Worked example 3 · Effect of doubling sampling resolution
An audio file uses 8-bit resolution. If resolution is doubled to 16-bit, what happens to file size?
Traps that cost marks every session
Trap · Describing sampling rate when the question asks about sampling resolution
These are DIFFERENT things. Rate = samples per second (Hz). Resolution = bits per sample. Cambridge routinely ask about one and get the other. Read the question — and if it says "resolution", talk about bits per sample.
Cited: 2024 examiner report — verbatim: "The most common incorrect answers describe sample rate instead of sample resolution"Trap · Saying "more accurate" without explaining HOW
Simply writing "higher sampling resolution means more accurate" is not enough for the mark. Explain the mechanism: a higher sampling resolution means a wider range of amplitudes can be recorded. For rate: more samples per second means more points on the waveform, so the shape is captured more accurately.
Cited: 2024 examiner report — verbatim: "Many candidates then repeated the question by stating that this made the recording more accurate without explaining how, that is, a higher sampling resolution means a wider range of amplitudes can be recorded"Trap · Applying "sampling resolution" to images
Sampling is about sound. Images use resolution (pixel count) and colour depth (bits per pixel) — different vocabulary. Do not describe pixels or colour when a sound question mentions "sampling resolution".
Cited: 2023 examiner report — verbatim: "Some candidates tried to describe the sample resolution in relation to an image"Trap · Confusing sampling rate with sampling frequency
They're the same thing, both measured in Hz. Sampling rate = sampling frequency = samples per second. Don't treat them as separate concepts.
Cited: recurring vocabulary patternTrap · Forgetting duration in the file size formula
File size = rate × resolution × duration. Miss the duration and your answer is per-second, not the whole file.
Cited: recurring formula-slip patternTrap · Answer in the wrong unit (bits vs bytes vs MiB)
Sound files are huge in bits. Read the question. Bytes = bits ÷ 8. KiB = bytes ÷ 1024. MiB = KiB ÷ 1024. Wrong unit = zero marks.
Cited: recurring exam-technique flagMark-scheme templates
These are the exact phrasings Cambridge accept. Learn them.
Check yourself — tap to reveal (0/6)
Answer these in your head, then tap to see the model answer. Aim for 5 or 6 right before moving on.
If you can answer 5 of the 6 knowledge checks above, you're ready to move on. Tap 🎓 Learn for the interactive content (including the 🎢 rollercoaster bridge), then 🎮 Activities for hands-on drills.
How sound becomes digital
Sound is analogue
Sound is a continuous wave — it changes smoothly and constantly. This is analogue data. Computers cannot store analogue data directly.
Sampling
The computer takes snapshots (samples) of the wave at regular intervals. Each sample records the amplitude (height) of the wave at that moment.
Stored as binary
Each sample's amplitude is converted to a binary number and stored. The sequence of binary values reconstructs an approximation of the original wave.
🎢 The rollercoaster bridge
Imagine photographing a rollercoaster ride. One photo per minute misses most of the action. One per second captures much more. More photos = better record of the ride. Sampling works the same way — more samples per second = closer to the original sound.
The two key concepts
Sampling rate
The number of samples taken per second.
Measured in Hz (Hertz) or kHz.
Higher rate → more samples → follows the wave more closely → more accurate → larger file.
Sampling resolution
The number of bits used to store each sample's amplitude.
Also called bit depth.
More bits → more possible amplitude values → amplitudes recorded more precisely → more accurate → larger file.
Two ways to improve accuracy
Cambridge regularly asks: "Give two ways to improve the accuracy of a sound recording." The answer is always:
1. Increase sampling rate
More samples per second → wave captured more frequently → closer to original.
2. Increase sampling resolution
More bits per sample → amplitude stored more precisely → closer to original.
File size and quality trade-off
The trade-off
Higher sample rate and higher resolution = better quality but larger file. Lower values = smaller file but lower quality. This is why compression exists — to reduce file sizes while keeping acceptable quality.
| Change | Quality | File size |
|---|---|---|
| ↑ Sample rate | Better (more samples) | Larger |
| ↑ Sampling resolution | Better (more precise) | Larger |
| ↓ Sample rate | Worse (fewer samples) | Smaller |
| ↓ Sampling resolution | Worse (less precise) | Smaller |
Quick check
What is sampling resolution?
Activity 1 — Rate vs Resolution Sorter
Is this describing sampling rate or sampling resolution?
Press New Question.
Activity 2 — Accuracy Improver
Name the improvement described.
Press New Question.
Activity 3 — Effect Predictor
What happens when this change is made?
Press New Question.
Adaptive practice
Press New Question.
Cambridge-style questions
Press New Question.
Review quiz
Press New.
Exam traps
Memory triggers
🧠 "Rate = how often, Resolution = how precise"
Rate is about frequency (per second). Resolution is about precision (bits per sample). Keep them separate in your mind.
🧠 "Rollercoaster photos"
More photos per second (rate) + higher quality photos (resolution) = best record of the ride. Same for sound sampling.
🧠 "Two marks, two improvements"
Whenever asked how to improve accuracy: (1) increase sampling rate (2) increase sampling resolution. Always give both.