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Sound Size Calculations

FoundationHigherAQA

Revise Sound Size Calculations for GCSE Computer Science with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA GCSE Computer Science (8525). Sound file size depends on the sample rate, the bit depth and the duration.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA specification. Every worksheet comes with a full mark scheme.

Foundation

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Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Sound file size is calculated from three quantities: the sample rate, the sample resolution and the duration.

The formula is file size = sample rate × sample resolution × duration in seconds. As with images the result is in bits, so divide by 8 for bytes and by a further 1000 for kilobytes.

The duration must be in seconds. A recording given in minutes must be multiplied by 60 first, and forgetting this makes the answer sixty times too small. A 10-second clip at 44 100 Hz and 16 bits gives 44 100 × 16 × 10 = 7 056 000 bits, which is 882 000 bytes, or 882 kilobytes.

Revision notes

The formula

File size = sample rate × sample resolution × duration in seconds.

The result is in bits. Divide by 8 for bytes, then by 1000 for kilobytes. Stereo recordings double the size, since two channels are stored.

Converting the duration

The duration must be in seconds before substituting.

A recording given in minutes must be multiplied by 60. Forgetting this gives an answer sixty times too small, which is the most frequent error in these calculations.

Working through an example

10 seconds at 44 100 Hz and 16 bits: 44 100 × 16 = 705 600 bits per second.

705 600 × 10 = 7 056 000 bits. Divided by 8 gives 882 000 bytes. Divided by 1000 gives 882 kilobytes.

Key points

  • File size = rate × resolution × duration.
  • The result is in bits.
  • Duration must be in seconds.
  • Multiply minutes by 60 first.
  • Divide by 8 for bytes.
  • Stereo doubles the file size.

Worked examples

Example 1

A 5-second clip is sampled at 8000 Hz with 8-bit resolution. Calculate the file size in bits. [3 marks]

Working

8000 × 8 = 64 000 bits per secondmultiply sample rate by resolution
64 000 × 5multiply by the duration in seconds
= 320 000 bitswork out the file size

Example 2

A recording lasts 2 minutes. State the duration to use in the formula and explain. [2 marks]

Working

120 secondsconvert to the required unit
because the formula requires the duration in seconds, so 2 × 60 = 120explain the conversion

Example 3

Convert a sound file of 320 000 bits into kilobytes. [3 marks]

Working

320 000 ÷ 8 = 40 000 bytesconvert bits to bytes
40 000 ÷ 1000convert bytes to kilobytes
= 40 kilobyteswork out the answer

Common mistakes

  • Using minutes instead of seconds.

    Multiply by 60 first — this is the most common error.

  • Forgetting the result is in bits.

    Divide by 8 for bytes.

  • Omitting the duration entirely.

    All three quantities are needed.

  • Ignoring stereo when stated.

    Two channels double the file size.

Exam tips

  • Convert the duration to seconds first.
  • Work out bits per second as a separate step.
  • Convert bits to bytes to kilobytes in order.
  • Double the result for stereo.

Key terms

Sample rate
Samples per second, in hertz.
Sample resolution
Bits used per sample.
Duration
The length of the recording in seconds.
Stereo
Two channels, doubling the file size.

Related topics

Written and reviewed against the current AQA specification. Spotted an error? Let us know.