Community resourceWorksheet

1CP2-P-9.4 Sound file size and fidelity trade-offs

Part 4 of 6 · 1CP2-P-9 · Bitmap, sound and compression

For mono uncompressed sound, size in bits is sample rate × bit depth × duration in seconds. The units are samples/second × bits/sample × seconds, leaving bits.

Students will:

  • construct the uncompressed sound-size expression
  • calculate in bits, bytes and binary storage units
  • rearrange the expression to find duration
  • explain fidelity and storage trade-offs precisely

Inside: 6 explanation cells, 1 fill-in-the-blanks cell, 2 multiple-choice questions and 3 written answers. 13 marks, about 45 minutes.

Series: 1CP2-P-9 · Bitmap, sound and compression, part 4 of 6.

Shared by Coding PathwayVerified teacher

  • 12 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 17 Aug 2026

Preview

The whole resource, exactly as a class sees it. Answers and marking are held back.

Sound file size and fidelity trade-offs

For mono uncompressed sound, size in bits is sample rate × bit depth × duration in seconds. The units are samples/second × bits/sample × seconds, leaving bits.

1. Build the representation

Sampling analogue soundanalogue waveform (blue); regular samples (orange)sample rate = samples each second; interval = time between samples

Convert minutes to seconds before multiplying. Convert bits to bytes by dividing by 8, then use 1024 for KiB. Rearrange the same relationship to find duration, rate or depth when the other values are supplied.

Fill in the blanks3 marks
Sound bits = sample gap 1 × bit gap 2 × duration in gap 3.
  • depth
  • rate
  • seconds
Multiple choice1 mark

Which expression gives the size of 10 seconds at 8000 samples/s and 8 bits/sample?

  • A8000 + 8 + 10
  • B8000 × 8 × 10
  • C8000 × 8 ÷ 10
  • D8000 ÷ 8 × 10

2. Worked method

For 8 seconds at 1024 samples/s and 8 bits/sample: 1024 × 8 × 8 = 65536 bits; divide by 8 to get 8192 bytes; divide by 1024 to get 8 KiB.

Written answer2 marks

Calculate the size in bits of 5 seconds sampled at 4000 samples/s with 8-bit depth.

Show formula and unit.

Students type their answer here.

Written answer3 marks

Convert 65536 bits into bytes and KiB.

Show both divisions.

Students type their answer here.

3. Apply and check

Write the formula or reasoning step before substituting values. Keep the representation, the measurement and its units distinct.

Written answer3 marks

A recording is 64000 bits, sampled at 1000 samples/s with 8-bit depth. Calculate its duration.

Rearrange the formula.

Students type their answer here.

Multiple choice1 mark

Which change gives more amplitude levels without changing samples per second?

  • AIncrease bit depth
  • BIncrease sample rate
  • CIncrease duration
  • DIncrease sample interval

Examination method

Show relevant working, label units and answer the command word. A number without its meaning or unit may not demonstrate the required method.

Route forward

Next you will choose between lossless and lossy compression from the need for exact reconstruction.