A sound wave changes smoothly and continuously, but a computer can only store separate binary numbers. So it measures the wave many times a second and stores each measurement. How often it measures, and how precisely, decides both the quality and the file size.
A sound wave is sampled: its amplitude (height) is measured at regular intervals and each measurement is stored as a binary number. The sample rate is the number of samples taken in a second (in hertz, Hz). The sample resolution is the number of bits per sample. Increasing either one makes the recording more accurate (closer to the original sound) but increases the file size.
Fig. 1: each blue dot is one sample of the sound wave, stored as a binary number
Section 01
Sampling the wave.
In the lab, look at the smooth sound wave and the samples taken from it. The computer keeps only the samples: the stepped line is what is played back.
Analogue to digital: sound is a continuous wave, so it has to be converted to binary before a computer can process it.
Sampling: the amplitude of the wave is measured at set time intervals.
Each sample is rounded to the nearest level the resolution allows and stored as a binary number.
Examiner trap
Say what is measured: the amplitude (height) of the sound wave, at regular time intervals. "The sound is recorded in binary" is too vague for a mark.
Section 02
Rate and resolution.
Increase the sample rate in the lab, then the resolution. Watch the stepped line get closer to the real wave, and the file size go up.
Sample rate
Sample resolution
Meaning
number of samples taken in a second
number of bits per sample
Unit
hertz (Hz); 44 100 Hz is CD quality
bits; 16 bits is CD quality
Increasing it
captures quicker changes in the wave
more amplitude levels: n bits give 2n levels
Effect
more accurate recording, but a larger file
Examiner trap
Doubling the resolution from 8 to 16 bits doubles the file size but gives 256 times as many levels (256 to 65 536). Do not mix the two up.
Stage 1 · Learn
Check what the sim just showed you
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What is the sample rate?
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What is the sample resolution?
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What happens when the sample resolution is increased?
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In the lab, what happens to the stepped line as the sample rate increases?
Section 03
Sound file size.
Each second stores (sample rate) samples, and each sample takes (resolution) bits. Multiply by the length of the track in seconds.
File size in bits = sample rate × sample resolution × length in seconds.
Then convert: ÷ 8 for bytes, ÷ 1024 for KiB, ÷ 1024 again for MiB.
Worked example Size of a recording
A 1-minute recording uses a sample rate of 8000 Hz and a sample resolution of 8 bits. Calculate its size in KiB.
Length = 60 seconds.
Bits = 8000 × 8 × 60 = 3 840 000 bits.
Bytes = 3 840 000 ÷ 8 = 480 000 bytes.
KiB = 480 000 ÷ 1024 = 468.75 KiB.
Answer: 468.75 KiB
Your turn
A 5-second sound has a sample rate of 1000 Hz and a resolution of 8 bits. How many bytes is it?
1000 × 8 × 5 = 40 000 bits; ÷ 8 = 5000 bytes
Stage 2 · Exam
Exam-style questions
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How many different amplitude levels can a 4-bit sample resolution store?
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The sample rate of a recording is doubled. What is the effect on the file size?
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Which settings give the most accurate recording?
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Why must sound be sampled before a computer can store it?
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