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CAIE 9618 · Paper 1 · Topic 1.1.6

Sound
Representation

Analogue vs Digital · Sampling Rate · Bit Depth · Nyquist Theorem · File Size

CSZone Cambridge International AS & A Level Computer Science 9618
Learning Objectives

By the end of this video you will be able to...

Explain the difference between analogue and digital sound
Define sampling rate and bit depth and state their effects on sound quality
State the Nyquist theorem and apply it
Calculate the file size of a sound recording
Analogue vs Digital

Converting Sound for a Computer

ANALOGUE SOUND
Continuous, smooth wave (pressure variation in air)
Infinite number of values in a given range
Represented by a microphone as a continuous electrical signal
DIGITAL SOUND
Discrete values — a series of numbers
The analogue signal is sampled at regular intervals
Each sample is stored as a binary number
An ADC (Analogue-to-Digital Converter) performs the conversion. A DAC converts digital back to analogue for playback.
Sampling Rate

How Often Do We Measure the Sound?

The sampling rate is the number of samples taken per second, measured in Hertz (Hz) or kHz. Higher sampling rate → better sound reproduction.
COMMON SAMPLING RATES
8,000 Hz — telephone quality
22,050 Hz — FM radio quality
44,100 Hz — CD quality (standard)
48,000 Hz — professional audio
96,000 Hz — high-definition audio
EFFECT ON QUALITY
Higher rate → more samples → better quality
Higher rate → larger file size
Low rate loses high-frequency details
Bit Depth (Sample Resolution)

How Precisely Do We Measure Each Sample?

Bit depth (also called sample resolution) is the number of bits used to store each sample. More bits → finer amplitude detail → better quality.
COMMON BIT DEPTHS
8-bit → 256 amplitude levels
16-bit → 65,536 levels (CD quality)
24-bit → 16,777,216 levels (studio)
EFFECT
More bits → less quantisation noise
Better dynamic range (quiet to loud)
Larger file size
Nyquist Theorem

The Minimum Sampling Rate

Nyquist Theorem: To accurately reproduce a sound of frequency f, the sampling rate must be at least 2f (twice the highest frequency in the signal).
Human hearing range: ~20 Hz to 20,000 Hz
Minimum rate to capture all human-audible sound: 2 × 20,000 = 40,000 Hz
CD standard: 44,100 Hz — slightly above the Nyquist minimum for safety
File Size Formula

Calculating Sound File Size

SOUND FILE SIZE FORMULA
File size (bits) = sampling rate × bit depth × duration (s) × channels
Mono = 1 channel · Stereo = 2 channels
WORKED EXAMPLE: 3-minute stereo CD audio
44,100 Hz × 16 bits × 180 s × 2 channels
= 254,016,000 bits
÷ 8 = 31,752,000 bytes ≈ 31.75 MB
Exam Practice

Cambridge-style questions

Question 1
A sound recording is made with a sampling rate of 22,050 Hz, a bit depth of 16 bits, and lasts 60 seconds. It is a mono recording. Calculate the file size in megabytes.
3 marks
✓ MARK SCHEME
1 mark
22,050 × 16 × 60 × 1 = 21,168,000 bits
1 mark
÷ 8 = 2,646,000 bytes
1 mark
÷ 1,000,000 = 2.646 MB
Exam Practice
Question 2
State the Nyquist theorem and explain why CD audio uses a sampling rate of 44,100 Hz.
3 marks
✓ MARK SCHEME
1 mark
The sampling rate must be at least twice the highest frequency to be recorded
1 mark
The highest frequency humans can hear is approximately 20,000 Hz
1 mark
44,100 Hz is above the minimum of 2 × 20,000 = 40,000 Hz, ensuring all human-audible frequencies are captured
Common Mistakes

Don't lose easy marks

1
Forgetting to multiply by the number of channels — stereo audio has 2 channels. If the question says "stereo", multiply by 2. Mono = 1 channel (no multiplication needed).
2
Confusing sampling rate with bit depth — sampling rate = how often samples are taken (Hz). Bit depth = how many bits per sample. Both affect quality and file size differently.
3
Stating the Nyquist theorem incorrectly — the sampling rate must be "at least twice" the highest frequency, not "the same as" or "greater than". The word "twice" is essential.
4
Saying higher sampling rate causes distortion — it does NOT. Higher sampling rate improves quality. What causes distortion is a rate that is too low (aliasing). Don't confuse cause and effect.
Topic Summary — 1.1.6

What You Need to Know

KEY TERMS
Sampling rate: samples per second (Hz)
Bit depth: bits per sample
ADC: converts analogue to digital
DAC: converts digital back to analogue
Nyquist: rate ≥ 2 × highest frequency
CD STANDARD
Sampling rate: 44,100 Hz
Bit depth: 16 bits
Channels: 2 (stereo)
Human hearing max: 20,000 Hz
FILE SIZE FORMULA
Bits = rate × bit depth × duration × channels
Bytes = bits ÷ 8
MB = bytes ÷ 1,000,000
Increasing rate OR depth → larger file
Increasing rate OR depth → better quality
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Next Video

1.1.7
Data Compression and Encryption
Lossy · Lossless · RLE · Huffman · Caesar Cipher
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