Representing Text, Sound, Images and Storage: Question 10
Syllabus 1.2, 1.3
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]
Show worked solution Hide worked solution
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