Representing Sound

Sound is an analogue signal — it varies continuously. Computers, however, work with digital (discrete) data. This lesson explains how sound is converted from analogue to digital and the factors that affect the quality and file size of digital audio.

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Analogue vs Digital

• Analogue signals are continuous — they change smoothly over time. Real-world sound waves are analogue.
• Digital signals are discrete — they are made up of distinct, separate values. Computers store data digitally as binary numbers.

To store sound on a computer, the analogue sound wave must be converted into a digital representation through a process called sampling.

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Sampling

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

The device that converts an analogue sound signal into digital data is called an Analogue-to-Digital Converter (ADC). To play digital sound back through speakers, a Digital-to-Analogue Converter (DAC) is used.

How Sampling Works

1. The sound wave is measured at regular time intervals.
2. At each interval, the amplitude (volume level) of the wave is recorded.
3. Each amplitude measurement is stored as a binary number.
4. When played back, the binary values are converted back into an analogue signal that approximates the original sound.

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Sample Rate

The sample rate (also called sampling frequency) is the number of samples taken per second. It is measured in Hertz (Hz).

• 1 Hz = 1 sample per second
• 1 kHz = 1000 samples per second
• 44.1 kHz = 44,100 samples per second (CD quality)

A higher sample rate means:

• More samples are taken each second.
• The digital representation is closer to the original analogue wave.
• The sound quality is better (more accurate reproduction).
• The file size is larger because more data is stored.

A lower sample rate means:

• Fewer samples per second.
• The digital representation is a rougher approximation of the original.
• The sound quality is lower.
• The file size is smaller.

Nyquist's Theorem

To accurately capture a sound, the sample rate should be at least twice the highest frequency in the audio. Human hearing ranges from about 20 Hz to 20,000 Hz, so CD audio uses a sample rate of 44,100 Hz (just over twice 20,000 Hz).

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Bit Depth (Sample Resolution)

Bit depth (also called sample resolution or bit resolution) is the number of bits used to store each individual sample.

Bit Depth	Number of Possible Values	Precision
8 bits	256 levels	Low quality
16 bits	65,536 levels	CD quality
24 bits	16,777,216 levels	Studio quality

A higher bit depth means:

• Each sample can be recorded more precisely (more possible amplitude levels).
• The sound quality is better — quieter sounds and subtle details are captured more accurately.
• The file size is larger.

A lower bit depth means:

• Fewer amplitude levels, so measurements are rounded to the nearest available value.
• This rounding introduces quantisation error — a slight distortion compared to the original.
• The sound quality is lower.
• The file size is smaller.

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Sound Digitisation Pipeline

flowchart LR
    A[Analogue sound wave] --> B[ADC samples wave]
    B --> C[Sample rate Hz]
    B --> D[Bit depth per sample]
    C --> E[Binary values stored]
    D --> E
    E --> F[File size = rate x depth x time x channels]

Calculating Audio File Size

The file size of a sound file can be estimated using:

File size (bits) = Sample rate (Hz) × Bit depth (bits) × Duration (seconds)

For stereo audio (two channels), multiply by 2:

File size (bits) = Sample rate × Bit depth × Duration × Number of channels

Worked Example 1

A mono audio clip is recorded at 44,100 Hz with a bit depth of 16 bits for 30 seconds.

• File size = 44,100 × 16 × 30 = 21,168,000 bits
• 21,168,000 ÷ 8 = 2,646,000 bytes
• 2,646,000 ÷ 1024 ≈ 2583.98 KB
• 2583.98 ÷ 1024 ≈ 2.52 MB

Worked Example 2

A stereo audio clip is recorded at 22,050 Hz with a bit depth of 8 bits for 10 seconds.

• File size = 22,050 × 8 × 10 × 2 = 3,528,000 bits
• 3,528,000 ÷ 8 = 441,000 bytes
• 441,000 ÷ 1024 ≈ 430.66 KB

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Effect of Sample Rate and Bit Depth

Change	Effect on Quality	Effect on File Size
Increase sample rate	Better quality (closer to original)	Larger file size
Decrease sample rate	Poorer quality (less accurate)	Smaller file size
Increase bit depth	Better quality (more precise samples)	Larger file size
Decrease bit depth	Poorer quality (more quantisation error)	Smaller file size

Exam Tip: Sound file size questions are very common. Remember the formula: sample rate × bit depth × duration (× channels if stereo). Always show your working and convert to appropriate units (bytes, KB, MB).

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Summary

• Sound is analogue; computers store it digitally by sampling the wave at regular intervals.
• Sample rate is the number of samples per second (Hz) — higher means better quality and larger files.
• Bit depth is the number of bits per sample — higher means more precise measurements and larger files.
• File size = sample rate × bit depth × duration (× channels for stereo).
• An ADC converts analogue to digital; a DAC converts digital to analogue.

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Extended Worked Examples

Worked Example 3: Compressed CD-quality recording

A 3-minute song is recorded at CD quality: 44,100 Hz sample rate, 16-bit depth, stereo (2 channels).

• Duration = 3 × 60 = 180 seconds
• Bits = 44,100 × 16 × 180 × 2 = 254,016,000 bits
• Bytes = 254,016,000 ÷ 8 = 31,752,000 bytes
• MB ≈ 31,752,000 ÷ 1024 ÷ 1024 ≈ 30.28 MB

This is the size of the uncompressed WAV file. Encoded as a 192 kbps MP3, the same song would be roughly 4.3 MB — about a seventh of the original size, with quality loss that most listeners cannot detect.

Worked Example 4: Voice recording for a podcast

A podcast records 30 minutes of mono speech at 22,050 Hz with 8-bit depth.