Representing Sound: Sampling Rate and Bit Depth

Sound is a continuous pressure wave — a vibration that travels through air (or another medium) and arrives at the ear as smoothly varying changes in air pressure. This is an analogue signal: it can take any value within a range, and it changes continuously with no gaps.

Computers can only store and process digital data — discrete binary values with no in-between states. To store sound on a computer, the continuous analogue signal must be converted into a sequence of discrete binary numbers. This conversion process is called analogue-to-digital conversion.

Property	Analogue sound	Digital sound
Values	Continuous — any value	Discrete — fixed steps
Storage	Cannot be stored directly	Stored as binary numbers
Quality loss	None in transmission	Depends on sampling settings

The higher the quality of the digital representation, the more closely it approximates the original analogue wave — and the more storage it requires.

Sampling is the process of measuring the amplitude (loudness) of a sound wave at regular intervals and recording each measurement as a binary number.

Each individual measurement is called a sample. The sequence of samples forms a digital approximation of the original wave.

The smooth curve is the original analogue wave. Each marked point is a sample — a measurement of the wave's amplitude taken at a fixed moment. The digital recording stores only those sampled values.

The accuracy of the digital representation depends on two factors:

1. How often samples are taken — the sampling rate
2. How precisely each sample is recorded — the sample resolution

A digital recording that uses many samples per second, each stored with many bits, closely matches the original wave. Fewer or less precise samples produce an approximation that loses detail.

Sampling rate is the number of samples taken per second. It is measured in hertz (Hz) or kilohertz (kHz).

A higher sampling rate captures more of the original wave's shape per second, producing a more accurate digital recording.

Sampling rate	Typical use
8,000 Hz	Telephone voice calls
22,050 Hz	Low-quality audio
44,100 Hz	CD-quality audio
96,000 Hz	Professional studio recording

Effect on quality and file size: doubling the sampling rate doubles both the accuracy of the recording and the amount of data generated per second. A 44,100 Hz recording captures 44,100 measurements every second — more than five times as many as an 8,000 Hz telephone recording.

(Extra context — not required by AQA 8525) Sampling rate must be at least twice the highest frequency present to avoid distortion. Human hearing reaches approximately 20,000 Hz, which is why CD audio uses 44,100 Hz.

Sample resolution (also called bit depth) is the number of bits used to store each individual sample. It determines how precisely the amplitude of the wave can be recorded.

More bits per sample means more possible amplitude values, producing a more accurate representation of volume changes.

The number of distinct amplitude levels is $2^{\text{sample resolution}}$:

Sample resolution	Amplitude levels	Typical use
8 bits	256	Low-quality audio, voice
16 bits	65,536	CD-quality audio
24 bits	16,777,216	Professional studio recording

Worked example — how many amplitude levels does 16-bit audio provide?

$2^{16}=65,536\text{ distinct levels}$

With 8-bit resolution, only 256 levels are available. Quiet passages that fall between two of those 256 steps are rounded to the nearest level, producing a faint background hiss called quantisation noise. Higher bit depth makes those steps smaller and the noise imperceptible.

The uncompressed file size of a digital audio recording depends on three values: sampling rate, sample resolution, and duration.

$\text{File size (bits)}=\text{sampling rate}\times \text{sample resolution}\times \text{duration (seconds)}$

$\text{File size (bytes)}=\frac{\text{sampling rate}\times \text{sample resolution}\times \text{duration}}{8}$

Worked example — a 10-second recording at 8,000 Hz with 8-bit resolution:

$\frac{8,000\times 8\times 10}{8}=\frac{640,000}{8}=80,000\text{ bytes}=80\text{ kB}$

Worked example — 60 seconds of CD-quality mono audio (44,100 Hz, 16-bit):

$\frac{44,100\times 16\times 60}{8}=\frac{42,336,000}{8}=5,292,000\text{ bytes}=5.292\text{ MB}\approx 5.3\text{ MB}$

The formula gives the uncompressed file size. Audio formats such as MP3 apply compression to reduce this significantly, but the uncompressed value is what AQA 8525 expects you to calculate.

Increasing either sampling rate or sample resolution improves audio quality but increases file size proportionally.

Change	Effect on file size	Effect on quality
Double the sampling rate	× 2	More faithful wave shape
Halve the sampling rate	÷ 2	Loss of high frequencies
Double the sample resolution	× 2	More precise volume levels
Halve the sample resolution	÷ 2	Audible quantisation noise

Worked example — compare two 30-second mono recordings:

Version	Sampling rate	Sample resolution	File size
A	8,000 Hz	8-bit	$(8,000\times 8\times 30)÷8=240,000\text{ bytes}$
B	44,100 Hz	16-bit	$(44,100\times 16\times 30)÷8=2,646,000\text{ bytes}$

Version B produces audio roughly 11 times larger than Version A. Whether that quality difference matters depends on the application — a voice call can tolerate Version A quality; a music recording cannot.

1. Confusing sampling rate with sample resolution

Sampling rate is how often samples are taken (Hz). Sample resolution is how many bits each sample uses. They are independent — a recording can have a high sampling rate but low resolution, or vice versa.

2. Forgetting to divide by 8

The formula produces an answer in bits. Divide by 8 to convert to bytes. The mark is usually awarded for the byte value, not the bit value, unless the question specifies otherwise.

3. Using the wrong unit for sampling rate

Sampling rate is measured in Hz (samples per second). A rate of 44.1 kHz is 44,100 Hz — not 44,100 kHz. Check that you are substituting the correct number into the formula.

4. Saying higher sampling rate always produces better quality

A higher sampling rate captures the wave shape more accurately, but if the sample resolution is very low, the amplitude at each sample point is still poorly recorded. Both values must be adequate for high-quality audio.

5. Multiplying by 2 for stereo without being asked

Stereo audio has two channels and therefore doubles the file size. Only apply the × 2 factor if the question explicitly states the recording is stereo.