Representing sound: File size (bits) = rate x res x secs

The idea

Sound is captured by sampling: measuring the wave at regular instants and storing each measurement as a binary number. The total storage needed, in bits, is found by multiplying three quantities: the sampling rate (samples taken each second, in Hz), the resolution (bits stored per sample, sometimes called bit depth), and the duration in seconds. So file size in bits = rate × resolution × seconds. For example, 8,000 samples per second at 8 bits per sample for 4 seconds gives 8,000 × 8 × 4 = 256,000 bits. Dividing by 8 converts bits to bytes, and dividing again by 1,000 (or 1,024) converts to kB. Always keep units consistent: seconds for time, Hz for rate, bits for resolution, and state that the answer is in bits before converting.

What earns the marks

• Identify the three factors that multiply together: sampling rate, resolution (bit depth) and duration in seconds.
• State that the product gives file size in bits, and that dividing by 8 gives bytes.
• Substitute values correctly, for example 8,000 Hz × 8 bits × 4 s = 256,000 bits.
• Convert between bits, bytes and larger units accurately, keeping the direction of each conversion correct.
• Recognise that increasing rate, resolution or duration increases file size proportionally.

Common mistakes and how to put them right

• Adding the three quantities instead of multiplying them.

  Put it right: The correct method multiplies rate, resolution and seconds together.

• Mixing units, such as using minutes for time or bytes for resolution.

  Put it right: Convert everything to seconds, Hz and bits first.

• Forgetting to convert the bit total to bytes or kB when the question asks for storage in those units.

  Put it right: Divide by 8 for bytes and then by 1,000 or 1,024 as required.

Exam tips

• Write the formula down first, then substitute numbers, so the method is visible even if arithmetic slips.
• Label the final answer with its unit (bits, bytes or kB) and check the question's requested unit.
• Sanity-check magnitude: a longer duration or higher rate must give a larger file size.