KS3 · Computer Science

Representing sound in binary

A song on your phone isn't sound at all: it's numbers. Ten seconds of stereo music is over fourteen million bits. Here's where every one comes from.

Computing · Representing sound

This is what the computer actually stores

16 audio samples at 4 bits, 16 levels, 44100 hertz, 1 channels

Sample 1 of 16
Levels16Bit depth4-bitSample rate44100 Hz
drag across the bars to redraw the wave

Each bar is one sample: a single measurement of the sound wave. With 4 bits per sample, each one is a whole number from 0 (0000) to 15 (1111), the 16 levels. The first sample is level 8, stored as 1000. Reshape the wave and you change the stored numbers, and the numbers ARE the sound the speaker plays back. What doesn't change: 16 samples × 4 bits = 64 bits, whatever you draw. 44100 Hz means 44,100 samples a second, so this strip is under half a thousandth of a second of sound.

From air to bits, and back to air

Watch the sound change form at each stage. The microphone and the speaker do the same job in opposite directions.

  2. A pressure wave travelsThose ups and downs in air pressure are the sound wave. Sound is a wave of changing air pressure.
  4. The device samples and stores itThe device measures that voltage over and over, and stores each measurement as bits. Now the sound is data: a long run of binary numbers.
  5. Back to electricityTo play the sound, the device turns the stored digital data back into electrical signals.

Two settings that get mixed up

Sample ratevsSample resolution (bit depth)

Rate is about HOW OFTEN. Resolution is about HOW PRECISELY.

Focus

The question it answers

Sample rate

How often is the wave measured?

Sample resolution (bit depth)

How accurately is each measurement stored?

The insight

This is the difference people swap most. One setting is about time, the other is about precision.

What it counts

Sample rate

The number of samples taken per second

Sample resolution (bit depth)

The number of bits used to store each sample

In the strip of bars

Sample rate

More bars packed into every second

Sample resolution (bit depth)

More possible heights for each bar

A typical value

Sample rate

44,100 samples per second

Sample resolution (bit depth)

16 bits per sample

Turn it up and…

Sample rate

The sound quality is generally better

Sample resolution (bit depth)

The sound quality also improves

Predict, then check

A channel is a single stream of audio. Mono has one, stereo has two, surround sound has more.

You save the same piece of music three times: in mono, in stereo and in surround sound. The sample rate and bit depth stay the same. What happens to the file size?

Your turn to fill the gaps

How big is ten seconds of stereo music?

A 10-second piece of music is recorded in stereo, at a sample rate of 44,100 samples per second and a sample resolution of 16 bits. How big is the file in bits, in bytes and in kilobytes? (Use 1 kilobyte = 1,000 bytes.)

  1. What we know: sample rate 44,100 samples per second, 16 bits per sample, duration 10 seconds, 2 channels (stereo).Before any multiplying, list the four numbers that decide the size.
  2. missing step
Which line is step 2?

Spot the slip

One line of this answer is wrong. Which one?

A 2-minute mono recording uses a sample rate of 8,000 samples per second and a sample resolution of 8 bits. Find its size in kilobytes (1 kilobyte = 1,000 bytes).

A student's answer — which line goes wrong?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

A computer can't keep a sound wave. What it keeps is measurements of the wave, thousands every second, each one written in binary.

What you need to know

  • Digital devices represent sound as sequences of bits (binary digits).
  • Sound is a wave: vibrations make air particles squeeze together and spread apart, creating variations in air pressure.
  • A microphone turns variations in air pressure into variations in voltage; a speaker turns variations in voltage back into variations in air pressure.
  • A sample is a single measurement of the sound wave, and each sample is stored as bits.
  • File size in bits = sample rate × sample resolution × duration (in seconds) × number of channels.

The big picture

Digital devices represent sound as sequences of bits. Sound is a wave of changing air pressure; a microphone turns it into changing voltage, the device samples that signal and stores each sample as bits, and on playback the data becomes electrical signals again for a speaker to turn back into air pressure. Sample rate is how many samples are taken each second; sample resolution (bit depth) is how many bits store each sample. Higher settings and more channels give better or fuller sound but bigger files. Size in bits = sample rate × sample resolution × duration × number of channels; divide by 8 for bytes.

Key points

1High air density means high pressure; low density means low pressure. The pattern of changing pressure is the sound wave.
2Sample rate is the number of samples taken per second (typically 44,100). It decides how often the wave is measured.
3Sample resolution, or bit depth, is the number of bits used to store each sample (typically 16). It decides how accurately each sample's amplitude is recorded.
4A channel is a single stream of audio: mono has one, stereo has two (left and right), and surround sound uses several, from speakers around the listener.
5Raising the sample rate or the bit depth generally improves quality, and adding channels gives fuller sound, but all three make the file bigger.
6One byte is 8 bits, so divide bits by 8 to get bytes. In this lesson, 1 kilobyte = 1,000 bytes.

Worked example

Problem

A music app saves a 30-second clip in stereo, at 44,100 samples per second and 16 bits per sample. (a) How big is the file in kilobytes (1 kilobyte = 1,000 bytes)? (b) The app's data-saver setting records the same clip in mono with 8 bits per sample instead. How big is it now, and what is the cost?

⚠ Watch out

Mixing up sample rate and sample resolution. Sample rate is how many samples are taken each second (like 44,100 per second). Sample resolution, or bit depth, is how many bits store each sample (like 16 bits). If a question says 'bits per sample', that's the resolution, not the rate.

🧠

Memory hook

Rate is how OFTEN, resolution is how PRECISELY. For the size: Rate × Depth × Duration × Channels, then ÷ 8 for bytes.

✓

Check yourself

Cover the page. A stereo clip is 3,000 kilobytes. Without a calculator, how big is it in mono at the same settings? Then say what sample rate and sample resolution each mean.

Flashcards

(12)
How do digital devices represent sound?
As sequences of bits (binary digits).
What is a sound wave, physically?
Vibrations make air particles squeeze together and spread apart, creating variations in air density and air pressure (high density = high pressure).
What does a microphone do?
It converts variations in air pressure into variations in electric voltage, so a device can capture the sound.
What does a speaker (or headphones) do?
It converts variations in electric voltage into variations in air pressure, which we hear as sound.
What is a sample?
A single measurement of an analogue signal, such as a sound wave. Each sample is stored as bits.
Sample rate
The number of samples taken per second: how often the wave is measured. Typical value: 44,100 samples per second.
Sample resolution (bit depth)
The number of bits used to store each sample: how accurately the amplitude is recorded. Typical value: 16 bits.
What is an audio channel?
A single stream of audio used to reproduce sound. One file can contain more than one channel.
Mono, stereo, surround: how many channels?
Mono: one channel, the same sound to every speaker. Stereo: two, left and right. Surround: several, from speakers placed around the listener.
What happens to file size when quality goes up?
Better quality (higher sample rate or bit depth) needs more storage. More channels also make the file bigger.
Formula for sound file size in bits
Sample rate × sample resolution × duration (seconds) × number of channels.
How do you turn bits into kilobytes?
Divide by 8 to get bytes (1 byte = 8 bits), then divide by 1,000 to get kilobytes.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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