GCSE · Computer Science · AQA · Spec 8525

Sampling sound

A sound wave is smooth, with no gaps. Now imagine you may only keep a list of numbers. How much of the wave could you get back?

Computer Science · Digital sound

The wave has gone. Only these bars are left.

16 audio samples at 3 bits, 8 levels, 8 hertz, 1 channels

Sample 1 of 16

Levels8Bit depth3-bitSample rate8 Hz

drag across the bars to reshape the recording

Each bar is one sample: the wave's amplitude, measured at one moment and kept. Here the wave is measured 8 times a second (8 Hz), so 16 bars cover 2 seconds. Each amplitude is stored as a 3-bit binary number, so only 8 levels exist, 0 to 7 (level 5 is stored as 101, level 2 as 010). Paint across the strip, or pick a bar and use the arrow keys, then try to set a bar to level 3½. Notice that nothing joins the bars: between two samples, nothing is stored.

Watch out: A digital recording is the list of measurements, not the wave itself. Whatever the wave did between two samples was never recorded.

Computer Science · Digital sound

Real wave or stored recording?

Is each description about the real analogue sound wave, or about the digitised sound a computer stores?

Still to sort

Analogue sound wave (0)

The real wave, as it travels

Where the line is: Continuous: no steps, no gaps, any value in its range.

Digitised sound (0)

What the computer actually keeps

Where the line is: Separate: set moments, set values, all stored as binary.

5 of 5 still to sort.

You have just seen what is left after sampling. Now decide which side of the line each description belongs to.

Predict, then check

Same wave, two recordings. Commit to an answer before you reveal it.

Recording A samples a wave 4 times each second. Recording B samples the same wave 16 times each second. Which statement is true?

Computer Science · Digital sound

What is a digital recording, really?

You record a friend's voice on your phone, then play it back.

Which is closest to what you think the stored recording is?

It's an exact copy of the sound, just written down as numbers.A higher sampling rate makes the recording louder.The computer keeps a smooth copy of the wave, just in a different format.It's a sequence of measurements. It misses what the wave did between samples, and each amplitude is stored to limited precision.

How sure are you?

I'm sureI think soI'm guessing

It's an exact copy of the sound, just written down as numbers.

This is a common misconception

Nearly, but not quite. The recording is a list of measurements. Whatever the wave did between two samples was never recorded, and each amplitude is stored with a limited number of bits, so it has to sit on one of a fixed set of levels. A faster sampling rate makes the gaps smaller. It never removes them.

A higher sampling rate makes the recording louder.

This is a common misconception

The sampling rate is how many measurements are taken each second. A higher rate gives more samples, so a closer copy and a bigger file. It does not make the amplitude values any larger.

The computer keeps a smooth copy of the wave, just in a different format.

This is a common misconception

No smooth copy is kept anywhere. Binary can only hold separate values, so what is stored is a sequence of numbers, one for each sample.

It's a sequence of measurements. It misses what the wave did between samples, and each amplitude is stored to limited precision.

This matches the evidence

Yes. That is exactly why digital sound is an approximation, and why measuring more often gets it closer.

A digital recording is a sequence of measurements, not the wave itself. That makes it an approximation of the original sound.

Computer Science · Digital sound

Say it in your own words

Describe, in order, what a computer does to store a sound as binary data. [3 marks]

Your answer

0 words · your answer stays on this page and is not sent anywhere.

The mark scheme

It measures the amplitude of the sound wave at regular intervals (it samples the wave). (1 mark)
Each measurement (sample) is stored as a binary number. (1 mark)
The binary numbers are kept as a sequence, in the order they were measured. (1 mark)

Model answer

The computer measures how big the wave is, the amplitude, at regular, equally spaced moments. Each measurement is turned into a binary number. The sequence of binary numbers is stored in the order they were measured.

Measure at regular intervals, turn each measurement into a binary number, keep the sequence.

Exam line: A good description follows the order the computer works in.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

A real sound wave is analogue: it varies smoothly and its amplitude can take any value.
A computer can only store binary, so it measures the amplitude at regular intervals. Each measurement is a sample.
Each sample is stored as a binary number, and the stored sound is the sequence of those numbers in order.
The sampling rate is the number of samples taken each second, measured in hertz (Hz).
A higher sampling rate gives a closer copy and a bigger file. A lower rate gives a smaller file and a rougher copy.
A digital recording is an approximation: the wave between samples is not recorded, and each amplitude is stored to limited precision.

The big picture

A sound wave is analogue: it changes smoothly and its amplitude can take any value. A computer can only store binary, so it measures the amplitude at regular, equally spaced moments and stores each measurement as a binary number. Those measurements are called samples, and the number taken each second is the sampling rate. A higher rate gives a closer copy but a bigger file. Either way the result is an approximation, because what the wave does between samples is lost and each amplitude is stored with limited precision.

Key points

1Sampling = measuring the amplitude of the wave at regular, equally spaced times.

2Each sample becomes a binary number. The list of numbers is the recording.

3Sampling rate = samples per second (Hz). It is how often you measure, not a property of the wave.

4More samples per second: closer to the original, bigger file. Fewer: smaller file, rougher copy.

5Digital sound is never an exact copy. It misses what happens between samples.

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Worked example

Problem

A sound wave is sampled six times. Each amplitude is rounded to a whole level from 0 to 7, which fits in three bits (place values 4, 2 and 1). The measured levels, in order, are 1, 4, 6, 7, 5 and 2. Write down what is stored.

⚠ Watch out

Thinking a digital recording is an exact copy of the sound. It is a sequence of measurements that misses what the wave does between samples. A related slip is thinking a higher sampling rate makes the sound louder. The rate only says how often the wave is measured.

🧠

Memory hook

Sampling is snapshots, not video. Take a photo every fraction of a second and you can flick through them like a film, but you never see what happened between the photos. The picture breaks down in one place: a sample is a number, not a photo.

✓

Check yourself

Cover the page and explain to an imaginary friend: when a computer records a sound, what exactly does it keep, and what does it lose?

Flashcards

(11)

What is an analogue sound wave?

A wave that varies smoothly and continuously, and whose amplitude can take any value.

Why can a computer not store a sound wave as it is?

It can only store binary values, so the smooth wave has to be measured and each measurement turned into a binary number.

What is sampling?

Measuring the amplitude of a sound wave at regular, equally spaced moments.

What is a sample?

One measurement of the wave's amplitude at one moment, stored as a binary number.

What does a digitised sound actually consist of?

A sequence of binary numbers, one per sample, in the order they were measured.

What is the sampling rate?

The number of samples taken each second, measured in hertz (Hz).

What does a sampling rate of 44,100 Hz mean?

44,100 samples are taken every second. It is one example of a sampling rate.

What happens if the sampling rate goes up?

The recording gets closer to the original sound, but the file gets bigger.

What happens if the sampling rate goes down?

The file gets smaller, but the recording is a rougher copy that misses more of the wave.

Is a digital recording an exact copy of the sound?

No. It is an approximation: the wave between samples is not recorded, and each amplitude is stored to limited precision.

Does a higher sampling rate make a recording louder?

No. The rate is how often the wave is measured, not how large its amplitude is.

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The wave has gone. Only these bars are left.

Real wave or stored recording?

What is a digital recording, really?

Say it in your own words

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