← IGCSE Computer Science Paper 1

Hertz and kilohertz

Sample rate is measured in hertz (Hz), the number of samples per second. 1 kHz is 1000 Hz, so 44.1 kHz is 44100 Hz. Frequency uses 1000, not 1024.

Part of: IGCSE Computer Science 0478 — 1.3 Data Storage and Compression — Module 24, ACARA Digital Technologies Years 7–8 — Representing Text, Images and Sound — Module 52

Understanding Hertz and kilohertz in IGCSE Computer Science Paper 1

What it does: The unit Hz shows the sample rate counts samples per second, so 8000 Hz means 8000 samples every second. The conversion multiplies the kHz value by 1000 to get Hz, ready to use in a file size calculation. Kilo means 1000 here. Hertz is a frequency unit, not a storage unit, so it does not use 1024. Divide by 1000 to convert Hz to kHz: 22050 / 1000 = 22.05 kHz. Converting kHz to Hz means multiplying by 1000, which gives 44100 Hz, not 441 Hz.

Common mistakes: The rate is in samples per second, so the total number of samples is rate_hz multiplied by seconds, not added. It should be samples ← rate_hz * seconds. kHz is a frequency unit, so 1 kHz is exactly 1000 Hz. 1024 is only used for storage units. It should be rate_hz ← rate_khz * 1000.

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Learning
Duo
Sample rate is measured in which unit?
Hertz (Hz), samples per secondBytes per second
Matches
1 kHz = 1024 Hz
↓
Kilohertz uses 1000, not 1024. 1024 is for storage units such as KiB. It should be 1 kHz = 1000 Hz.
Applying
Meanings
Term
1 kHz = 1000 Hz
Meaning
Sample rate is measured in hertz (Hz), the number of samples per second. 1 kHz is 1000 Hz, so 44.1 kHz is 44100 Hz. Frequency uses 1000, not 1024.
Practice
rateKHz <- 44.1
Testing
Gaps
Sample rate is measured in
Check Answer
Spots
3seconds ← 10
4samples ← rate_hz + seconds

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Quick Questions

1. Sample rate is measured in which unit?
A. Hertz (Hz), samples per second ✓
B. Bytes per second
Sample rate counts how many samples are taken each second, and that is measured in hertz (Hz).
2. How many hertz are in 1 kHz?
A. 1024 Hz
B. 1000 Hz ✓
Kilo means 1000 here. Hertz is a frequency unit, not a storage unit, so it does not use 1024.
3. What is 44.1 kHz written in hertz?
A. 44100 Hz ✓
B. 441 Hz
Multiply by 1000: 44.1 x 1000 = 44100 Hz, so 44100 samples are taken every second.
4. A sound is sampled at 8 kHz. How many samples are taken each second?
A. 8192
B. 8000 ✓
8 kHz = 8 x 1000 = 8000 Hz. Use 1000, not 1024, for frequency.
5. Why does kHz use 1000 instead of 1024?
A. It is a frequency unit, not a storage unit ✓
B. Because computers always use 1000 for everything
Only storage units such as KiB and MiB use 1024. Frequency units such as Hz and kHz use 1000.

Match the Pairs

1 kHz = 1000 Hz → One kilohertz is 1000 samples per second, because frequency units use 1000.
44.1 kHz = 44100 Hz → A CD-quality sample rate of 44100 samples taken every second.
Sample rate is measured in hertz, which means samples per second → sample_rate = 8000 Hz
Convert kHz to Hz before calculating by multiplying by 1000 → Hz = kHz * 1000
1 kHz = 1024 Hz → Kilohertz uses 1000, not 1024. 1024 is for storage units such as KiB. It should be 1 kHz = 1000 Hz.
44.1 kHz = 441 Hz → The value was not multiplied by 1000 correctly. 44.1 x 1000 = 44100, so it should be 44.1 kHz = 44100 Hz.

Key Term

1 kHz = 1000 Hz
Sample rate is measured in hertz (Hz), the number of samples per second. 1 kHz is 1000 Hz, so 44.1 kHz is 44100 Hz. Frequency uses 1000, not 1024.

Fill in the Blanks

1. Sample rate is measured in Hz
Hint: Type the unit symbol for samples per second.
2. 44.1 kHz = 44100 Hz
Hint: Type the sample rate in hertz after converting from kilohertz.
3. khz <- 22.05 hz <- khz * 1000
Hint: Type the multiplier for a frequency unit, not a storage unit.
4. 1 kHz = 1000 Hz
Hint: Type the unit symbol that means one thousand hertz.
5. 1 Hz = 1 sample per second
Hint: Type the word for what is counted each second in a sound recording.

Spot the Error

Question 1
A rate_khz ← 44.1
B rate_hz ← rate_khz * 1000
C seconds ← 10
D samples ← rate_hz + seconds
E OUTPUT samples
Line D — The rate is in samples per second, so the total number of samples is rate_hz multiplied by seconds, not added. It should be samples ← rate_hz * seconds.
Question 2
A rate_khz ← 8
B rate_hz ← rate_khz * 1024
C OUTPUT rate_hz
Line B — kHz is a frequency unit, so 1 kHz is exactly 1000 Hz. 1024 is only used for storage units. It should be rate_hz ← rate_khz * 1000.
Question 3
A // 1 kHz is 1000 Hz
B rate_khz ← 22.05
C rate_hz ← rate_khz / 1000
D OUTPUT rate_hz
Line C — Going from kHz to Hz means multiplying by 1000, because Hz is the smaller unit. Dividing would give a number that is far too small. It should be rate_hz ← rate_khz * 1000.
Question 4
A rate_hz ← 22050
B rate_khz ← rate_hz * 1000
C OUTPUT rate_khz
Line B — Going from Hz to kHz means dividing by 1000, because kHz is the larger unit. Multiplying would give a huge wrong value. It should be rate_khz ← rate_hz / 1000.
Question 5
A rate_khz ← 16
B rate_hz ← rate_khz * 1000
C OUTPUT "Sample rate:"
D OUTPUT rate_hz, "kHz"
Line D — rate_hz holds a value in hertz (16000), so the label must be "Hz". Labelling 16000 as kHz would mean 16 million Hz. It should be OUTPUT rate_hz, "Hz".

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