Lesson 5 of 6 · Data & Binary
Representing Sound
Sound is a continuous analogue wave. Computers store a digital approximation. The quality of that approximation depends on two settings -- and you can hear the difference.
Explain how analogue sound is converted to digital using sampling
Define sample rate (Hz) and explain its effect on quality and file size
Define bit depth and explain its effect on quality and file size
Calculate sound file size using the formula
Analogue to digital: the problem
Sound is a pressure wave that travels through air. It is analogue: it varies continuously and can take any value at any point in time -- there is no gap between possible values.
Computers store information as binary numbers -- discrete, stepped values. To store sound digitally, the computer must convert the continuous analogue wave into a series of numbers. This process is called sampling.
At each sample point, the computer measures the amplitude (height) of the sound wave and records it as a binary number. The wave between sample points is discarded. The resulting series of numbers is the digital representation of the sound.
Sample rate and bit depth
Two settings control how accurately a digital recording represents the original analogue sound:
Sample rate: The number of samples taken per second, measured in Hertz (Hz). A sample rate of 44,100 Hz (44.1 kHz) means 44,100 amplitude measurements per second. Higher sample rate = more faithful reproduction of rapid changes in the wave = better quality = larger file.
Bit depth: The number of bits used to store each sample's amplitude value. More bits = more possible amplitude levels = smoother, more accurate wave = better quality = larger file. CD quality uses 16 bits (65,536 amplitude levels).
| Setting | Low value | High value | Trade-off |
|---|---|---|---|
| Sample rate | 8,000 Hz (telephone quality) | 44,100 Hz (CD quality) | Higher = better quality, larger file |
| Bit depth | 8 bits (256 levels) | 16 bits (65,536 levels) | Higher = less quantisation noise, larger file |
Fill-in-the-gaps exam answer: Sound sampling is when the amplitude of the sound wave is measured at set intervals. The sample rate is the number of times per second the wave is measured, given in Hertz. Each amplitude is stored as a unique binary number. The number of bits allocated to each sample is the bit depth. The higher the bit depth, the wider the range of amplitudes that can be measured.
Calculating sound file size
Sound file size formula:
File size (bits) = Sample rate × Bit depth × Duration (seconds)
File size (bytes) = File size (bits) ÷ 8
For stereo (2 channels): multiply the result by 2.
File size (bits) = Sample rate × Bit depth × Duration (seconds)
File size (bytes) = File size (bits) ÷ 8
For stereo (2 channels): multiply the result by 2.
Example: A 3-minute stereo recording at 44,100 Hz sample rate and 16-bit depth.
Duration in seconds: 3 × 60 = 180 seconds
File size (bits) = 44,100 × 16 × 180 = 126,720,000 bits
File size (bytes) = 126,720,000 ÷ 8 = 15,840,000 bytes
For stereo: 15,840,000 × 2 = 31,680,000 bytes
In MB: 31,680,000 ÷ 1,048,576 = 30.2 MB (uncompressed WAV)
MP3 compression reduces this to about 3-4 MB at typical quality.
Waveform Sampler
Waveform Sampler
Interactive + Live AudioAdjust sample rate and bit depth. The waveform visualises how accurately the samples capture the original wave. Press Play to hear the difference using your browser's audio engine.
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Samples per second
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Amplitude levels
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Size per second (bytes)
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Quality tier
Lower qualityHigher quality
Exam Focus
- Sampling measures AMPLITUDE (height of the wave), not frequency. Mixing these up is the most common error on this topic.
- Sample rate is measured in Hertz (Hz) or kilohertz (kHz). 44,100 Hz = 44.1 kHz. Always state the unit.
- Fill-in-the-gap questions: the missing words are typically "analogue", "sampling", "sample rate", "unique", and "bit depth". Learn these exact terms.
- File size calculation: state units at every step. The formula gives bits -- divide by 8 for bytes, then by 1024 for KB.
- Effect of bit depth question: "Increasing bit depth increases the number of amplitude levels that can be stored, producing a higher-quality recording with less distortion, but the file size increases."
Check your understanding
1. Which of the following correctly describes sound sampling?
Sampling measures AMPLITUDE (height) of the analogue wave at set time intervals. Frequency is a property of the wave itself, not what sampling measures.
2. A recording has a sample rate of 8,000 Hz and bit depth of 8 bits. What is the file size in bytes for 1 minute of audio?
8,000 samples/sec x 8 bits x 60 seconds = 3,840,000 bits. 3,840,000 / 8 = 480,000 bytes (mono). This is telephone quality audio.
3. Explain how changing the bit depth affects the sound file.
Bit depth determines how many distinct amplitude values can be stored per sample (2^n levels). More levels = finer amplitude resolution = less quantisation noise = better quality. But each sample uses more bits, so the file is larger.
4. What unit is the sample rate measured in?
Sample rate is measured in Hertz (Hz) -- the number of samples per second. CD quality is 44,100 Hz (44.1 kHz).
5. A musician has 1,000 recordings with an average file size of 3 MB each. What total storage is needed in GB?
1,000 x 3 MB = 3,000 MB. 3,000 / 1,024 = approximately 2.93 GB. Using 1 GB = 1,024 MB is the standard approach in these questions.
Think Deeper
The Nyquist theorem states that to accurately capture a sound wave, the sample rate must be at least twice the highest frequency in the audio. Human hearing tops out at about 20,000 Hz. Why is CD quality set at 44,100 Hz rather than just 40,000 Hz?
44,100 Hz provides a safety margin above the theoretical 40,000 Hz minimum. In practice, the analogue filter needed to remove frequencies above half the sample rate (the "anti-aliasing filter") is not perfectly sharp -- it has a gradual roll-off. Starting at 44,100 Hz gives extra room so the filter can roll off between 20,000 Hz and 22,050 Hz without introducing audible artefacts in the 20 Hz-20,000 Hz range. The 44,100 Hz figure was also influenced by early digital audio being stored on video tape (which had convenient timing based on NTSC and PAL frame rates).
Streaming music services send compressed audio (MP3, AAC, FLAC) rather than uncompressed WAV. A 3-minute uncompressed stereo track is about 30 MB. At 320 kbps MP3 quality, it is about 7 MB. What kind of compression is this, and what information is discarded?
MP3 uses lossy compression. It applies a psychoacoustic model -- a model of human hearing -- to identify and discard audio information that the ear is unlikely to notice. The main techniques include: removing frequencies that are masked by louder sounds at nearby frequencies (simultaneous masking), removing sounds that occur just after a louder sound (temporal masking), and using coarser encoding for frequency ranges where the ear is less sensitive (below 80 Hz and above 16,000 Hz). The discarded data cannot be recovered. FLAC, by contrast, is lossless -- the original data can be perfectly reconstructed, but files are typically 50% of the uncompressed size rather than 25%.
Printable Worksheets
Practice what you've learned
Three printable worksheets covering sound and sampling at three levels: Recall, Apply, and Exam-style.
Recall
Worksheet 1
Key term matching + audio quality table + file size formula • 16 marks
Apply
Worksheet 2
File size calculations for CD and voice recordings • 17 marks
Exam-style
Worksheet 3
Extended sampling, Nyquist theorem and evaluation questions • 20 marks
Exam Practice
Lesson 5: Sound Representation
5 MCQ with instant feedback + 3 written questions with mark schemes.
Teacher Panel
Lesson 5 -- Representing Sound
Lesson Objectives
Explain that sampling converts an analogue wave to digital by measuring amplitude at set intervals
Define sample rate (measurements per second, in Hz) and bit depth (bits per sample)
Explain that higher sample rate and higher bit depth both improve quality and increase file size
Calculate file size using: sample rate x bit depth x duration / 8 = bytes
Complete fill-in-the-gap questions about sound representation using correct terminology
Timing Guide
0-5 min: Play two clips -- high quality vs telephone quality. Ask: what is different? (Primes amplitude/frequency discussion)
5-12 min: Sampling concept, analogue vs digital wave diagram, amplitude definition
12-20 min: Sample rate and bit depth -- definitions, units, effect on quality and file size
20-27 min: File size calculation -- worked example with units at each step
27-35 min: Waveform Sampler tool -- students change settings and hear the result
Common Misconceptions
"Sampling measures the frequency of the wave" -- sampling measures AMPLITUDE. Frequency is a property of the wave; sample rate is a property of the recording process. These are different things.
"Higher sample rate means higher pitch" -- sample rate determines how often amplitude is measured; it does not change the pitch of the stored sound (within normal ranges).
"Bit depth is the same as colour depth for images" -- the analogy is useful but imprecise. Bit depth here controls amplitude precision; colour depth controls colour palette size. Both increase quality and file size.
Confusing sample rate (Hz = samples/second) with bit depth (bits per sample). Both are needed in the file size formula and both have independent effects on quality.
Marking Guidance
Fill-in-the-gap (6 marks): The standard question uses: analogue, sampling, sample rate, unique, bit depth, higher. Practise this exact sequence. Award 1 mark per correct term.
Effect of bit depth (2 marks): 1 mark for quality effect (more amplitude levels, less distortion), 1 mark for file size effect (larger). Both must be addressed. "Better quality" alone = 1 mark maximum.
File size calculation: Must show sample rate x bit depth x time in seconds, then / 8 for bytes. Missing units on the final answer = no marks for that step.
The Waveform Sampler Activity
Students set sample rate to minimum (500 Hz) and bit depth to 1 bit, then press Play. The audio is heavily distorted. Ask: what is causing the distortion? (Low bit depth = only 2 amplitude levels; sound is heavily quantised.) Then increase bit depth to 16, keeping sample rate low. The pitch quality improves but rapid changes are still missed. Finally, increase both to maximum -- the sound becomes clear. This sequence makes the two independent effects directly audible.
Exit Tickets
Fill in the gaps: sound [sampling] measures the [amplitude] of the wave at set intervals. The [sample rate] is given in [Hertz]. Each amplitude is stored as a [unique] binary number. [2 marks -- checks key vocabulary]
Calculate the file size in bytes of 1 minute of mono audio at 44,100 Hz and 16-bit depth. [2 marks]
Explain how increasing bit depth affects the sound quality and file size. [2 marks]
Differentiation
Grade 4 Define sampling and sample rate. State that higher values = better quality AND larger file. Fill-in-the-gap practice.
Grade 7 Explain bit depth independently. File size calculation in bytes. Compare mono vs stereo storage requirements.
Grade 9 Discuss the Nyquist theorem principle (sample rate must be at least 2x the highest frequency). Explain why MP3 compression reduces file size by discarding psychoacoustically redundant information.