Representing Text, Sound, Images and Storage: Question 10

Syllabus 1.2, 1.3

Structured 8 marks

A podcast studio records an interview in stereo, meaning two separate audio channels (left and right) are sampled at the same time, rather than the single channel used for a mono recording. Both channels use a sample rate of 44,100 Hz and a sample resolution of 16 bits. The recording lasts exactly 2 minutes.

(a) State how many channels are recorded in this stereo recording, and explain why recording in stereo affects the file size compared with a mono recording made with the same sample rate, sample resolution and duration. [2]

(b) Calculate the file size of the 2-minute stereo recording, in bytes. Show all your working. [4]

(c) Give the file size of the recording in mebibytes (MiB), to 2 decimal places. [2]

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Worked solution

Part (a): Number of channels and effect on file size

A stereo recording captures 2 channels (left and right) at the same time, whereas a mono recording captures only 1 channel. Each channel is sampled and stored independently using the same sample rate and sample resolution, so a stereo recording stores two complete sets of samples instead of one. As a result, a stereo recording made with the same sample rate, sample resolution and duration as a mono recording has twice the file size of the mono recording.

Part (b): Calculating the file size in bytes

The file size, in bits, of a sound recording is found using:

file size (bits) = sample rate x sample resolution x duration (seconds) x number of channels

First, convert the duration to seconds:

2 minutes = 2 x 60 = 120 seconds

Substituting the values given (sample rate 44,100 Hz, sample resolution 16 bits, duration 120 seconds, 2 channels):

44,100 x 16 = 705,600

705,600 x 120 = 84,672,000

84,672,000 x 2 = 169,344,000 bits

Convert bits to bytes by dividing by 8:

169,344,000 / 8 = 21,168,000 bytes

So the stereo recording is 21,168,000 bytes.

Part (c): Converting to mebibytes (MiB)

A mebibyte is 1024 x 1024 = 1,048,576 bytes, so divide the file size in bytes by 1,048,576:

21,168,000 / 1,048,576 = 20.1874...

Rounding to 2 decimal places:

So the recording is 20.19 MiB.

Final answers

  • (a) 2 channels; stereo doubles the file size compared with mono at the same settings.
  • (b) File size = 21,168,000 bytes
  • (c) File size = 20.19 MiB