1.2.2 Representing Sound
A microphone detects continuously changing air pressure. A computer, however, stores discrete binary values. Digital recording therefore involves taking selected measurements from the incoming signal and encoding those measurements as numbers.
By the end of this section, you should be able to:
- distinguish continuous analogue sound from discrete digital sound data;
- describe how sampling converts a changing signal into a sequence of values;
- use the terms sampling rate and sampling resolution accurately;
- explain how each setting affects recording accuracy and the amount of data stored;
- compare recording settings and justify a suitable choice for a given use.
Exam tip: explain the chain of cause and effect
Avoid writing only “the quality improves”. State what changes first, then connect it to the result. For example: more samples are taken each second, so rapid changes in the signal are represented more closely, but more values must also be stored.
From a Sound Wave to Binary Data
The conversion can be understood as a four-stage pipeline. The stages are related, but each answers a different question: what is detected, when it is measured, which stored level is chosen, and how that level is represented inside the computer.
| Stage | What happens | Result |
|---|---|---|
| Capture | A microphone changes variations in air pressure into an electrical signal. | A continuously changing analogue signal |
| Sample | The signal amplitude is measured at evenly spaced moments. | A sequence of measurements |
| Quantise | Each measurement is matched to the nearest available amplitude level. | A discrete numerical level |
| Encode | The selected level is stored as a binary value. | Digital sound data |
Digital data: data represented using a limited set of discrete values, normally encoded in binary.
A small numerical example
Suppose one measurement has an amplitude of approximately 5.7 units, but the encoder can store only whole-number levels. The value may be quantised to level 6. With a 5-bit code, that level could be stored as 00110. The stored number is close to the measurement, but it is not identical to it.
Common mistake: treating analogue and digital as quality labels
These words describe how data varies, not whether a recording is automatically good or bad. Analogue data is continuous; digital data uses separate encoded values.
Sampling: Choosing Moments to Measure
Sampling means measuring the amplitude of the signal at regular time intervals. The computer stores the sample values rather than every point on the original wave.
Example: a short wildlife recording
A field recorder samples a bird call at 12,000 samples per second. During a 0.25-second section, it takes:
12,000 × 0.25 = 3,000 samples
If the rate is increased to 24,000 samples per second, the same 0.25-second section contains 6,000 measurements. The second recording has more information about how the signal changes over time, but it also stores twice as many sample values.
Common mistake: saying that sampling stores the complete wave
A sample is one measurement at one moment. The complete digital recording is a sequence of measurements that approximates the continuous signal between them.
Two Independent Recording Settings
Students often confuse sampling rate with sampling resolution because both influence accuracy and storage. A useful distinction is that rate controls the horizontal detail in time, while resolution controls the vertical detail in amplitude.
| Setting | What it controls | Typical unit | What increases when the setting rises? |
|---|---|---|---|
| Sampling rate | How often the signal is measured | Hz or samples per second | The number of samples stored each second |
| Sampling resolution | How many bits are available for one sample | bits per sample | The number of possible amplitude levels |
Sampling rate
A higher rate places measurement points closer together in time. This can represent quicker changes in the waveform more faithfully. It also increases the number of stored values for every second of audio.
Sampling resolution
Sampling resolution is the number of bits used to encode one sample. With n bits, there are 2n possible codes and therefore the same number of available amplitude levels.
| Resolution | Calculation | Available levels | Interpretation |
|---|---|---|---|
| 5 bits | 25 | 32 | Large gaps between neighbouring levels |
| 9 bits | 29 | 512 | Measurements can be placed more precisely |
| 13 bits | 213 | 8,192 | Much finer amplitude steps |
Common mistake: reversing rate and resolution
Rate is the number of samples taken each second. Resolution is the number of bits used for each sample. “Bits per second” is not a definition of either term by itself.
Accuracy, Quantisation Error and Storage
A measured amplitude will not always match one of the available digital levels. The encoder chooses a nearby level, creating a small difference between the measured value and the stored value. This difference is called quantisation error.
Increasing the sampling resolution creates more levels with smaller gaps between them, so the stored value can usually be closer to the measurement. Increasing the sampling rate does not change the number of amplitude levels; instead, it creates more measurement points along the time axis.
| Change | Likely effect on accuracy | Effect on stored data |
|---|---|---|
| Increase sampling rate | Represents rapid changes in the signal more closely | More samples are stored per second |
| Increase sampling resolution | Reduces rounding between available amplitude levels | More bits are stored for every sample |
| Decrease either setting | May reduce the accuracy of the digital approximation | Reduces the amount of sound data |
Choosing settings for a purpose
A battery-powered voice logger may prioritise long recording time and intelligible speech, so moderate settings could be suitable. A studio recording intended for detailed editing may use higher settings because accuracy matters more and greater storage is available. The strongest justification links the choice to the needs and constraints of the situation.
Exam tip: use comparative language
When comparing two recordings, name the changed setting and explain both consequences. A useful structure is: “Recording B uses a higher ___, therefore ___; however, ___.”
Interactive: Sound Sampling Visualiser
Change the rate and resolution independently. Watch where measurements are taken and how each measurement is rounded to an available digital level.
Building a Strong Explanation
Question pattern 1: describe the encoding process
A complete response should connect the analogue input to the stored binary output: the signal is measured at regular intervals, each measurement is assigned to an available amplitude level, and the selected level is encoded as a binary value.
Question pattern 2: explain the effect of a change
Identify whether the change affects the number of measurements or the number of bits per measurement. Then connect that change to accuracy and storage.
| Weak statement | Stronger explanation |
|---|---|
| “The sound is better.” | “A higher sampling rate records more measurements each second, so short changes in the waveform can be represented more closely.” |
| “The file becomes bigger.” | “More samples are stored each second, so the amount of binary data increases for the same duration.” |
| “More bits make it accurate.” | “More bits per sample create more amplitude levels, reducing the rounding needed when a measurement is quantised.” |
Common mistake: giving an absolute claim
Do not claim that increasing a setting makes the recording identical to the original wave. It normally improves the approximation, but the representation remains discrete.
Optional Extensions
The ideas below are useful for deeper understanding and for connecting sound representation to later topics. They go beyond the core sound requirements of this section, so keep them separate from the essential definitions and explanations above.
Extension 1: Nyquist’s sampling rule
To represent a signal containing frequencies up to a chosen maximum, the sampling rate should be at least twice that maximum frequency.
minimum sampling rate = 2 × highest frequency
For a signal with a highest frequency of 6,400 Hz, the theoretical minimum is:
2 × 6,400 = 12,800 Hz
Extension 2: estimating uncompressed sound data
The raw amount of sound data can be estimated by multiplying the number of samples per second by the bits used for each sample, the duration, and the number of channels.
bits = sampling rate × sampling resolution × duration × channels
An 18-second mono recording made at 24,000 Hz with 10 bits per sample contains:
24,000 × 10 × 18 × 1 = 4,320,000 bits
4,320,000 ÷ 8 = 540,000 bytes
Common mistake: presenting an estimate as the exact final file size
This calculation covers uncompressed sample data. A real file may also contain a header, metadata or compressed data, so its final size can differ.
Practice
Core questions
- Explain why a continuously changing sound signal cannot be stored directly as a finite sequence of binary values.
- Describe the stages used to turn a microphone signal into digital sound data.
- Distinguish sampling rate from sampling resolution.
- A recorder takes 15,000 samples per second. How many samples are taken in 0.4 seconds?
- How many amplitude levels are available when 7 bits are used for each sample?
- Explain one accuracy benefit and one storage consequence of increasing the sampling rate.
- Explain one accuracy benefit and one storage consequence of increasing the sampling resolution.
- A school wants to record spoken announcements for a long-term archive. State one factor that would support using higher settings and one factor that would support using lower settings.
Optional extension questions
- A sound contains frequencies up to 8,750 Hz. Find the minimum rate suggested by Nyquist’s rule.
- Estimate the size in bytes of 25 seconds of stereo sound recorded at 16,000 Hz with 8 bits per sample.
- Explain why the calculated raw-data size may not equal the size shown by an actual audio file.