1.2.3 Sampling Sound Waves
A student podcast club records a short welcome message for the school website. The original voice is a changing sound wave. Before a computer can store or process the recording, the wave must be converted into binary data.
This is done by taking measurements of the sound wave at regular intervals. These measurements are called samples. Each sample is then represented using a binary value.
By the end of this section, you should be able to:
- explain why sound must be converted into binary data;
- describe sampling as measuring a sound wave at regular intervals;
- define sample rate and sample resolution;
- explain how sample rate affects recording accuracy and file size;
- explain how sample resolution affects recording accuracy and file size;
- apply these ideas to simple recording scenarios.
From sound wave to digital data
Real sound changes continuously. A microphone detects these changes and converts them into an electrical signal. The computer then needs a digital representation made from stored numbers.
Analogue 模拟: data that can vary continuously.
Digital 数字: data represented using discrete values, usually stored as binary.
| Stage | What happens | Result |
|---|---|---|
| 1. Original sound | A voice or instrument produces a changing sound wave | Continuous analogue sound |
| 2. Sampling | The wave is measured at regular time intervals | A sequence of sample values |
| 3. Binary representation | Each sample value is stored using bits | Digital sound data |
| 4. Playback | The stored values are used to reconstruct an approximation | Sound is produced again |
Common mistake
A recorded sound file does not store the original air vibration itself. It stores numeric measurements that can be used to approximate the sound when played back.
Sampling a sound wave
Sampling means taking measurements of the wave at regular intervals. Each measurement records the amplitude of the sound wave at that moment.
Amplitude 振幅: the height of the wave at a particular moment, related to the loudness of the sound.
Sampling 采样: taking repeated measurements from a wave so that it can be represented digitally.
If only a few samples are taken, the computer has limited information about the shape of the original wave. If more samples are taken, the recorded data can follow the shape more closely.
Answer-building tip
A strong answer explains both actions: the sound wave is measured repeatedly, and each measurement is stored as a binary value.
Sample rate
The sample rate tells us how many samples are taken every second.
Hertz 赫兹 (Hz): a unit meaning “per second”. For example, 8000 Hz means 8000 samples per second.
| Sample rate | Meaning | Samples in 5 seconds |
|---|---|---|
| 4000 Hz | 4000 samples per second | 20 000 samples |
| 8000 Hz | 8000 samples per second | 40 000 samples |
| 16 000 Hz | 16 000 samples per second | 80 000 samples |
Increasing the sample rate usually improves the accuracy of the recording because the wave is measured more often. However, it also creates more sample values to store.
Common mistake
Sample rate is about how often measurements are taken, not how many bits are used for each measurement.
Sample resolution
After a sample has been taken, its amplitude must be stored as a binary value. Sample resolution tells us how many bits are available for each sample.
Bit depth 位深度: another common term for the number of bits used to store one sample.
| Sample resolution | Calculation | Possible amplitude levels |
|---|---|---|
| 2 bits per sample | 22 | 4 levels |
| 3 bits per sample | 23 | 8 levels |
| 4 bits per sample | 24 | 16 levels |
| 8 bits per sample | 28 | 256 levels |
A higher sample resolution gives more possible values for each measurement. This can represent changes in amplitude more accurately, but each sample uses more bits.
Common mistake
Doubling the sample resolution does not merely double the number of amplitude levels. The number of possible levels is calculated using powers of two.
Worked example: a short sound clip
A one-channel sound clip is recorded for 6 seconds. It uses a sample rate of 12 000 Hz and a sample resolution of 8 bits per sample.
Step 1: calculate the number of samples
12 000 samples per second × 6 seconds = 72 000 samples
Step 2: calculate the sample data
72 000 samples × 8 bits = 576 000 bits
This is a simplified calculation for sample data only. A real sound file may also include additional information such as file format, sample rate, sample resolution and channel information.
Answer-building tip
Use the correct factor for the question: sample rate affects the number of samples, while sample resolution affects the number of bits per sample.
Accuracy and file size
Sample rate and sample resolution both affect the quality and amount of stored data.
| Change | Effect on recording accuracy | Effect on file size |
|---|---|---|
| Increase sample rate | The wave is measured more often, so the shape can be followed more closely | More samples are stored |
| Decrease sample rate | Fast changes in the wave may be missed | Fewer samples are stored |
| Increase sample resolution | Each sample can use more amplitude levels | More bits are stored for each sample |
| Decrease sample resolution | Amplitude values are rounded into fewer levels | Fewer bits are stored for each sample |
Develop the explanation
Avoid writing only “quality improves”. Explain why: a higher sample rate takes more measurements per second, so the recorded data can follow the wave more closely.
When sample values are rounded
A sample may not match exactly one of the available amplitude levels. The value must then be rounded to the nearest level that the chosen sample resolution can represent.
With a low sample resolution, there are fewer levels, so each sample may be rounded more noticeably. With a higher sample resolution, there are more possible levels, so the stored value can be closer to the measured amplitude.
Common mistake
A higher sample resolution does not take more samples per second. It gives each sample more possible values.
The computer also needs recording information
Stored sample values need context. Software must know how quickly to play them back and how each sample should be interpreted.
| Information | Why it matters |
|---|---|
| Sample rate | Controls how many stored samples are played each second |
| Sample resolution | Shows how many bits should be read for each sample value |
| Length | Helps calculate or interpret the duration of the recording |
| Number of channels | Shows whether the recording is mono, stereo or another format |
Common mistake
Playing the same sample data with the wrong sample rate could change the speed or pitch of the sound.
Choosing suitable recording settings
Higher settings are not always the best choice. The purpose of the recording matters.
| Scenario | Suitable priority | Reason |
|---|---|---|
| Short voice note for a classroom app | Smaller file size | Speech may still be understandable with moderate settings |
| Music recording for a performance archive | Higher accuracy | More detail in the sound should be preserved |
| Emergency alert tone | Clarity and quick transmission | The message must be recognisable without wasting bandwidth |
| Sound effect in a small game | Balance between quality and storage | Many sound effects may need to fit inside the application |
Use the scenario
In an exam-style explanation, link your choice to the situation. For example, a voice alert may not need the same accuracy as a music recording.
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.
Practice
Core questions
- Define the term sample.
- Explain why a sound wave must be sampled before it can be processed by a computer.
- Define the term sample rate.
- A recording uses a sample rate of 8000 Hz. How many samples are taken in 12 seconds?
- Define the term sample resolution.
- Calculate how many amplitude levels can be represented using 5 bits per sample.
- Explain how increasing the sample rate can improve recording accuracy.
- Explain why increasing the sample rate also increases file size.
- Explain how increasing sample resolution can improve recording accuracy.
- Explain why increasing sample resolution also increases file size.
- A short mono sound uses 20 samples per second for 4 seconds. Each sample uses 6 bits. Calculate the number of bits of sample data.
- Explain why a recording may need metadata such as sample rate and sample resolution.
Extension questions
- A student says, “A higher sample rate means each sample has more bits.” Explain the error.
- A 2-second mono recording uses 10 000 samples per second and 8 bits per sample. Calculate the number of bits of sample data.
- A recording changes from 8-bit samples to 16-bit samples while keeping the same sample rate and length. Explain the effect on accuracy and file size.
- A voice alert must be transmitted quickly over a slow connection. Explain why very high sample rate and resolution may not be suitable.
Check selected answers
- 8000 × 12 = 96 000 samples.
- 5 bits provide 25 = 32 amplitude levels.
- 20 × 4 × 6 = 480 bits of sample data.
- 10 000 × 2 × 8 = 160 000 bits of sample data.
- 16-bit samples provide 216 = 65 536 amplitude levels.
Review
Key ideas
- Sound is originally a changing wave.
- A computer represents sound by storing sampled measurements as binary data.
- A sample is one measurement of the wave.
- Sample rate is the number of samples taken each second.
- Sample resolution is the number of bits used for each sample.
- A higher sample rate can record the wave shape more accurately.
- A higher sample resolution can represent amplitude more accurately.
- Increasing either sample rate or sample resolution increases the amount of data.
- Stored sound data may need metadata such as sample rate and resolution.
Quick self-check
- Can I explain what sampling does?
- Can I distinguish sample rate from sample resolution?
- Can I explain why increasing sample rate improves accuracy?
- Can I explain why increasing sample resolution improves accuracy?
- Can I explain why higher settings increase file size?
One-minute exit task
Explain why a sound recorded at 16 000 Hz with 8-bit samples needs more sample data than the same sound recorded at 8000 Hz with 8-bit samples.