Sound representation: sampling, sample rate and bit depth

Computers are digital — they store everything as binary numbers. Sound, however, is an analogue phenomenon: a continuous wave of air pressure. To store sound digitally, it must be converted from analogue to digital using a process called sampling. OCR J277 tests sampling concepts and file size calculations.

How analogue sound is digitised

The analogue-to-digital conversion process

1. A microphone converts sound waves into an analogue electrical signal (a continuous wave).
2. An ADC (Analogue-to-Digital Converter) samples the amplitude (height) of the wave at regular time intervals.
3. Each sample is stored as a binary number representing the amplitude at that moment.
4. The result is a series of numbers — a digital approximation of the sound wave.

Playback (digital-to-analogue)

• On playback, a DAC (Digital-to-Analogue Converter) converts the digital numbers back into an analogue electrical signal.
• A speaker converts the electrical signal back into sound waves.

Key concepts

Sample rate (sampling frequency)

• The number of samples taken per second (measured in Hz or kHz).
• Higher sample rate → more samples per second → more accurate representation → better quality sound.
• CD quality: 44,100 Hz (44.1 kHz) — captures all frequencies audible to humans (up to 20 kHz).
• Phone quality: 8,000 Hz — adequate for speech but not music.
• Professional audio: 48,000 Hz or 96,000 Hz.

Bit depth (sample resolution)

• The number of bits used to store each sample — how precisely each amplitude value is recorded.
• Higher bit depth → more possible amplitude values → smoother, more accurate sound → better quality.
• 8-bit audio: 2⁸ = 256 possible amplitude levels.
• 16-bit audio (CD standard): 2¹⁶ = 65,536 possible levels.
• 24-bit audio (studio quality): 2²⁴ = 16,777,216 possible levels.

Channels

• Mono: 1 channel (one speaker).
• Stereo: 2 channels (left + right speakers) — doubles the file size compared to mono.

Calculating audio file size

Formula:

File size (bits) = sample rate x bit depth x duration (seconds) x number of channels
File size (bytes) = file size (bits) / 8

Worked example

A 3-minute stereo audio recording at CD quality (44,100 Hz, 16-bit):

• Duration: 3 x 60 = 180 seconds
• Sample rate: 44,100 samples/second
• Bit depth: 16 bits/sample
• Channels: 2 (stereo)

Size = 44,100 x 16 x 180 x 2 = 254,016,000 bits
     = 254,016,000 / 8 = 31,752,000 bytes
     = 31,752,000 / 1,000,000 ≈ 31.75 MB

Trade-offs

Increase	Effect on quality	Effect on file size
Higher sample rate	Better (more accurate)	Larger
Higher bit depth	Better (smoother)	Larger
More channels (stereo vs mono)	Better (spatial)	Larger

• Compression (e.g. MP3) reduces file size by discarding some audio data (lossy) or using algorithms that reduce redundancy (lossless — e.g. FLAC).

Common OCR exam mistakes

1. Confusing sample rate with bit depth — sample rate = samples per second; bit depth = bits per sample.
2. Forgetting to multiply by the number of channels for stereo.
3. Forgetting to divide by 8 to convert bits to bytes.
4. Saying "higher sample rate makes the sound louder" — it makes it more accurate/higher quality; volume is not affected.