Understanding Digital Sound Representation

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Understanding Digital Sound Representation

What do you already know about how computers represent sound?

Learning Objective

At the end of the lesson you will be able to explain how computers represent sound, use the OCR sound file size formula, and apply knowledge to exam scenarios.

Starter: Recap on Image Representation

Calculate the file size of a 7"x5" image at 300 PPI, with 8-bit colour depth. Step-by-step: 1. Find total pixels: (7×300) × (5×300) = 2,100 × 1,500 = 3,150,000 pixels 2. Each pixel uses 8 bits: 3,150,000 × 8 = 25,200,000 bits 3. Convert bits to bytes (÷8): 25,200,000 ÷ 8 = 3,150,000 bytes 4. Convert bytes to kilobytes (÷1,000): 3,150,000 ÷ 1,000 = 3,150 KB

Bridge: Connecting Images and Sound

Image Representation

Sound Representation

Pixels: smallest image elements Resolution: pixels per inch (PPI) Colour Depth: bits per pixel

Samples: smallest audio units Sample Rate: samples per second (Hz) Bit Depth: bits per sample

Key Definitions (OCR Spec)

Sample: The amplitude measurement of a sound wave at a set point in time. Sampling Frequency (Sample Rate): The number of audio samples captured per second, measured in Hertz (Hz). Sample Resolution (Bit Depth): The number of bits used to store each sample. Sample Size: The total data required for one sample, usually Sample Rate × Bit Depth.

The Sound File Size Formula

Size (bits) = Sample Rate (Hz) × Bit Depth (bits) × Duration (s) × Number of Channels For stereo, use channels = 2; for mono, channels = 1. Remember: OCR uses 1,000 for KB/MB conversions.

Worked Example 1: Mono Sound

Question: What is the file size of a 10-second mono recording at 22,050 Hz, 8-bit depth? Step 1: 22,050 × 8 × 10 × 1 = 1,764,000 bits Step 2: 1,764,000 ÷ 8 = 220,500 bytes Step 3: 220,500 ÷ 1,000 = 220.5 KB

Worked Example 2: Stereo Sound

Question: What is the file size of a 2-minute stereo recording at 44,100 Hz, 16-bit depth? Step 1: 44,100 × 16 × 120 × 2 = 169,344,000 bits Step 2: 169,344,000 ÷ 8 = 21,168,000 bytes Step 3: 21,168,000 ÷ 1,000 = 21,168 KB

Worksheet & Scenarios

Try 6 practice scenarios: • Bronze: 5s mono, 8,000 Hz, 8-bit • Silver: 10s mono, 22,050 Hz, 16-bit • Silver: 20s mono, 44,100 Hz, 16-bit • Gold: 1min stereo, 22,050 Hz, 16-bit • Gold: 2min stereo, 48,000 Hz, 24-bit • Challenge: 30min stereo, 96,000 Hz, 24-bit See the answer key for solutions and method.

Demo: Sampling and Clipping

Using AudioMass.co, zoom into a waveform to observe individual samples and the 'stepped' shape caused by sampling. Demonstrate clipping by increasing a signal’s volume until it flattens at the top – this shows digital limits.