Topics from the Cambridge IGCSE (9-1) Computer Science syllabus.

1.2.2 | SOUND REPRESENTATION

Topics from the Cambridge IGCSE (9-1) Computer Science 0984 syllabus 2023 - 2025.

OBJECTIVES
1.2.2 Understand how and why a computer represents sound, including the effects of the sample rate and sample resolution

ALSO IN THIS TOPIC
1.1.1 NUMBER SYSTEMS
1.1.2 NUMBER SYSTEMS
1.1.3 NUMBER SYSTEMS
1.1.4 NUMBER SYSTEMS
1.1.5 NUMBER SYSTEMS
1.1.6 NUMBER SYSTEMS
1.2.1 TEXT, SOUND AND IMAGES
YOU ARE HERE | 1.2.2 TEXT, SOUND AND IMAGES
1.2.3 TEXT, SOUND AND IMAGES
1.3.1 STORAGE AND COMPRESSION
1.3.2 STORAGE AND COMPRESSION
1.3.3 STORAGE AND COMPRESSION
1.3.4 STORAGE AND COMPRESSION
TOPIC 1 KEY TERMINOLOGY
TOPIC 1 ANSWERS
TOPIC 1 TEACHER RESOURCES (CIE)

DATA REPRESENTATION

WHAT IS SOUND ?

Sound is vibrations that oscillate in wave forms creating a change in pressure. Each wave is defined as a frequency, one oscillation can be seen in the diagram below.

Showing one full oscillation and a frequency of 18 Hertz

Frequency is measured in hertz. The diagram above shows one complete oscillation in 18 seconds, this means the wave have a frequency of 18 hertz.

Sound travels as an analogue wave and we need to convert the analogue wave into digital representation for computer use. When converting the analogue wave into digital format there are two main factors we need to consider.

How often do we want to take a sample of the original sound wave(times per second), this is known as sample rate.
At what points on the amplitude do we want to take a sample, the amount of points on the amplitude that we are able to take a sample is called the bit depth or resolution.

If we were looking to convert the above sound wave into digital, we can only take samples were the wave meets a bit depth point and we can only take samples on a predefined time per second. If we were to take 2 samples per second then we would have taken 36 samples of the one oscillation illustrated. These samples can only be recorded on one of the bit depth levels. As illustrated with the sample taken at 15 seconds (marked X).

The above diagram has a bit depth of 3, because 3 bits have been used to represent the amplitude, this would mean a maximum of 8 or 2^3 points on the amplitude could be digitally represented.

Note: The values used are just for illustration purpose, in practice you could expect a sample rate of about 40,000 and a bit depth of 32.

When considering what sample rate and what bit depth to use there are a few factors to influence this decision.

Nyquist's theorem - We need to sample a sound wave at double its highest frequency to be able to produce an accurate reproduction of the original.
The scope of the human ear - The human ear can hear between 20Hz and 20,000Hz, much of a sound wave will be out of this range and not worth recording anyway. A band-limiting filter if often used to clip frequency out of the 20Hz - 20,000Hz range.
The purpose of the recording and the medium through which it is used. - If the sound expected to be high quality and is to be played on a high quality sound system then a high sample rate and high bit depth is needed. If less quality is needed of it is to be streamed to platforms like youtube then a lower sample rate and bit depth would allow for faster data transfer.

According to Nyquist's theorem if a sound wave has a frequency of 10,000Hz we would need to sample at 20,000 samples per second to get an accurate reproduction of the original. Most CDs are recorded at 44,100 samples.

1: Fill in the blanks
A microphone captures sound in an analogue format, before the computer can represent this a .............................. is needed to convert the sound to a .................... format.
2: Describe what is meant by the term 'sampling'.
3: Explain why the sample rate effects the quality of the sound
4: Describe what is meant by the term 'bit depth'.
5: Describe what is meant by the term 'channel'.
6: Sound for youtube videos is often not represented at high quality, give 3 reasons why this might be the case for this scenario.

CALCULATING SOUND FILE SIZE

Samples per second x bits per second x time (in seconds)
or
Sample Rate X Bit Depth X Time
or for example
10,000(samples per second) X 16 (bit depth) X 60 (seconds) = 9,600,000 BITS

The result for the example above is shown in Bits but, it would be more appropriate to show the results in bytes, megabytes. To convert to a more appropriate representation, firstly you would divide by 8 to see how many bytes and then by 1024 for Kb and 1024 for Mb and so on..

9,600,000 / 8 = 1,200,000 Bytes
1,200,000 / 1024 = 1171.875 Kilo Bytes
1171.875 / 1024 = 1.14 Mega Bytes

1.4Mb is a much more appropriate term to use for the representation of the file size example above.

The above example presumes that the audio output is mono (the exact same sound is being sent to each speaker. Currently sound representation is at very least recorded in stereo, meaning that the left and right speaker work independently, if the sound is stored in stereo then the file size should be double. With larger home audio system a 5.1 representation could be expected, in this care each speaker has its independent sound track, Front Left, Front Center, Front Right, Rear Left, Rear Right and separate base speaker (subwoofer), in this case 6 channels may be needed so the file size could be 1.14Mb X 6. ( Check out the beach scene in 5.1 on the movie 'Saving Private Ryan' for a cool representation of 5.1 surround).

HOW DOES A MICROPHONE WORK

Internal working of a microphone

A microphone is a relative simple piece of technology using a transducer to convert movement to digital representation. It is like an inverted speaker, it uses a diaphragm to collect the sound, the diaphragm moves as waves of sound displace its position. It is delicately balanced to return to it neutral position after a sound wave has forced it to move. The diaphragm movement is connected a coil placed over a magnet this movement creates an electrical charge, as it movements alternates the electric current flowing alternates. This value can then be measured and converted into a digital representation of sound by measuring the frequency and depth of change.

Click here to check out how a microphone works

SOUND FILE SIZE

1: Calculate the file size for the following sound sample, give the size in MB

Mono
Sample rate: 42000
Bit Depth: 16bit
Time: 60 seconds

2: Calculate the file size for the following sound sample, give the size in MB

Stereo
Sample rate: 20000
Bit Depth: 16bit
Time: 120 seconds

3: What happens to the file size as more channels are represented?

4: Calculate the file size for the following sound sample, give the size in MB

4 channel
Sample rate: 44100
Bit Depth: 16
Time: 180

ALSO IN THIS TOPIC

1.1.1 NUMBER SYSTEMS | Why Computers use Binary
1.1.2 NUMBER SYSTEMS | Binary, Hex and converting between number systems
1.1.3 NUMBER SYSTEMS | Benefits of Hex
1.1.4 NUMBER SYSTEMS | Binary Addition and Overflow
1.1.5 NUMBER SYSTEMS | Binary Shifts
1.1.6 NUMBER SYSTEMS | Negative Number Representation, Two's Complement
1.2.1 TEXT, SOUND AND IMAGES | How Computers Represent Text
1.2.2 TEXT, SOUND AND IMAGES | How Computers Represent Sound
1.2.3 TEXT, SOUND AND IMAGES | How Computers Represent Images
1.3.1 STORAGE AND COMPRESSION | How Data Storage is Measured
1.3.2 STORAGE AND COMPRESSION | Calculating Image and Sound File Size
1.3.3 STORAGE AND COMPRESSION | Purpose of Data Compression
1.3.4 STORAGE AND COMPRESSION | Lossy and Lossless, how files are compressed
TOPIC 1 KEY TERMINOLOGY
TOPIC 1 ANSWERS
TOPIC 1 TEACHER RESOURCES (CIE)

NEXT PAGE | BINARY AND HEX