Representing Text, Sound, Images and Storage: Question 3

Worked solution

Part (a): Sample rate and sample resolution

When a computer records sound, it samples the analogue sound wave many times each second and stores each sample as a binary number.

• Sample rate is the number of samples taken per second.
• Sample resolution is the number of bits used to store each sample.

Part (b): Calculating the file size

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

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

Substituting the values given:

8000 x 16 x 3 = 384,000 bits

(check: 8000 x 16 = 128,000, and 128,000 x 3 = 384,000)

Convert bits to bytes by dividing by 8:

384,000 / 8 = 48,000 bytes

So the voice message is 48,000 bytes.

Part (c): Recalculating with a higher sample resolution

Using the same formula with the sample resolution increased to 32 bits, and the sample rate (8000 Hz) and duration (3 seconds) unchanged:

8000 x 32 x 3 = 768,000 bits

(check: 8000 x 32 = 256,000, and 256,000 x 3 = 768,000)

768,000 / 8 = 96,000 bytes

So the new file size is 96,000 bytes, exactly double the original file size, because doubling the sample resolution doubles the amount of data stored for every sample, while the sample rate and duration stay the same.

Part (d): Advantage and disadvantage of the higher resolution

Advantage: each sample is measured more precisely (more possible amplitude values per sample), so the recorded sound is a more accurate copy of the original analogue wave and sounds closer to the original.

Disadvantage: the file is larger (96,000 bytes instead of 48,000 bytes), so it takes longer to send over the network and uses more of the recipient’s storage space.

Final answers

• (a) Sample rate = number of samples per second; sample resolution = number of bits per sample.
• (b) File size = 48,000 bytes
• (c) New file size = 96,000 bytes
• (d) Advantage: better sound quality/accuracy. Disadvantage: larger file size (slower to send, more storage used).