Sound Representation: Sampling, Sample Rate, Bit Depth, and File Size

Computers store sound by taking samples of an analogue sound wave and converting them to digital data. This lesson covers how sound is digitised and how to calculate audio file sizes, as required by OCR J277 Section 2.6.

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Analogue vs Digital Sound

Analogue sound is a continuous wave — the air vibrates smoothly, producing a wave with infinite detail. Digital sound is a series of discrete numerical values that approximate the original wave.

To convert analogue sound to digital, a computer uses an ADC (Analogue-to-Digital Converter). The ADC measures the amplitude (height) of the sound wave at regular intervals. Each measurement is called a sample.

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Sampling

Sampling is the process of measuring the amplitude of a sound wave at regular time intervals. Each sample is stored as a binary number.

The quality of the digital recording depends on two factors:

1. Sample rate — how often samples are taken
2. Bit depth — how many bits are used to store each sample

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Sample Rate

The sample rate is the number of samples taken per second, measured in Hertz (Hz).

Sample rate	Samples per second	Use
8,000 Hz (8 kHz)	8,000	Telephone quality
22,050 Hz	22,050	Radio quality
44,100 Hz (44.1 kHz)	44,100	CD quality
48,000 Hz (48 kHz)	48,000	DVD/professional audio
96,000 Hz (96 kHz)	96,000	Studio quality

A higher sample rate captures the sound wave more accurately because more measurements are taken, producing a closer approximation to the original analogue wave.

OCR Exam Tip: CD quality audio uses a sample rate of 44,100 Hz. This number appears frequently in exam questions — memorise it.

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Bit Depth

Bit depth (also called sample resolution) is the number of bits used to store each individual sample. More bits means a wider range of amplitude values can be recorded.

Bit depth	Number of levels	Use
8 bits	2^8 = 256	Low quality (telephone)
16 bits	2^16 = 65,536	CD quality
24 bits	2^24 = 16,777,216	Professional studio

A higher bit depth means:

• More possible amplitude values per sample
• Better representation of quiet and loud sounds
• Less quantisation error (the difference between the actual amplitude and the stored value)

flowchart LR
    A[Analogue sound wave] --> B[Microphone]
    B --> C[ADC - Analogue to Digital Converter]
    C --> D[Sample at rate Hz]
    D --> E[Quantise to bit depth]
    E --> F[Binary samples stored]
    F --> G[File size = rate x depth x duration x channels]
    G --> H[Optional compression - MP3 / AAC]
    H --> I[Stored audio file]

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How Sampling Works: A Visual Explanation

Imagine a smooth sound wave. The ADC takes readings at regular intervals:

Amplitude
    |     *  *
    |   *      *
    |  *   |    *   |    Samples taken at marked intervals
    | *    |     *  |
    |*     |      * |
    +------+-------+-------> Time

The more frequently we sample (higher sample rate), the more dots we plot, and the closer our digital version matches the original wave.

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File Size Calculation for Sound

The formula for calculating the file size of an uncompressed audio file:

File size (bits) = sample rate x bit depth x duration (seconds)

For stereo (2 channels): multiply by 2 For multi-channel (e.g., 5.1 surround = 6 channels): multiply by 6

Worked Example 1: Mono Audio

A mono recording is 30 seconds long, with a sample rate of 44,100 Hz and a bit depth of 16 bits.

Step	Calculation	Result
Total bits	44,100 x 16 x 30	21,168,000 bits
Bytes	21,168,000 / 8	2,646,000 bytes
Kilobytes	2,646,000 / 1024	2,583.98 KB
Megabytes	2,583.98 / 1024	2.52 MB

Worked Example 2: Stereo Audio

A stereo recording is 3 minutes (180 seconds) long, at 44,100 Hz, 16-bit depth.

Step	Calculation	Result
Total bits	44,100 x 16 x 180 x 2	254,016,000 bits
Bytes	254,016,000 / 8	31,752,000 bytes
Megabytes	31,752,000 / (1024 x 1024)	30.28 MB

OCR Exam Tip: Always state the formula before substituting values. Remember to multiply by the number of channels (1 for mono, 2 for stereo). Forgetting the channels is a common mistake.

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Effect of Changing Audio Properties

Change	Effect on quality	Effect on file size
Increase sample rate	Better quality (more accurate)	Larger file
Decrease sample rate	Lower quality (less accurate)	Smaller file
Increase bit depth	More amplitude levels, less noise	Larger file
Decrease bit depth	Fewer levels, more quantisation noise	Smaller file
Increase duration	N/A (longer recording)	Larger file

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MIDI vs Sampled Sound

OCR J277 may also refer to MIDI (Musical Instrument Digital Interface):

Feature	Sampled sound	MIDI
Stores	Actual audio samples	Musical instructions (notes, duration, volume)
File size	Large	Very small
Editing	Difficult to edit individual notes	Easy to edit notes, tempo, instruments
Quality	Depends on sample rate/bit depth	Depends on the synthesiser/sound bank
Voice recording	Yes	No

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Worked Example: Comparing Podcast Storage at Three Quality Levels

A broadcaster is evaluating three quality presets for a 20-minute mono podcast. Calculate the storage required for each, and discuss the trade-offs.

Setup: duration = 20 minutes = 1,200 seconds, channels = 1 (mono).

Preset A — telephone quality: 8,000 Hz sample rate, 8-bit bit depth.

• Total bits: 8,000 x 8 x 1,200 = 76,800,000 bits.
• Bytes: 76,800,000 / 8 = 9,600,000 bytes.
• KB: 9,600,000 / 1024 = 9,375 KB.
• MB: 9,375 / 1024 = 9.16 MB.

Preset B — radio quality: 22,050 Hz sample rate, 16-bit bit depth.

• Total bits: 22,050 x 16 x 1,200 = 423,360,000 bits.
• Bytes: 423,360,000 / 8 = 52,920,000 bytes.
• KB: 52,920,000 / 1024 = 51,679.69 KB.
• MB: 51,679.69 / 1024 = 50.47 MB.

Preset C — CD quality: 44,100 Hz sample rate, 16-bit bit depth.