ExpertMedium2 marksStructured
AQA GCSE · Question 13.3 · Fundamentals of data representation
A 50-second sound has been recorded at a sample rate of 40 000 Hz. Two bytes have been used to store each sample of the sound. Calculate the file size of the sound file in megabytes. Show your working.
A 50-second sound has been recorded at a sample rate of 40 000 Hz. Two bytes have been used to store each sample of the sound. Calculate the file size of the sound file in megabytes. Show your working.
How to approach this question
1. **Identify the variables:**
* Duration = 50 seconds
* Sample rate = 40,000 Hz
* Bytes per sample (Sample resolution) = 2 bytes
2. **Calculate the total file size in bytes:** Use the formula: `File size (bytes) = Sample Rate × Duration × Bytes per Sample`.
3. **Perform the calculation:** `40,000 * 50 * 2`.
4. **Convert to megabytes (MB):** The result will be in bytes. To convert to kilobytes (KB), divide by 1000. To convert from KB to MB, divide by 1000 again. So, divide the total bytes by 1,000,000.
Full Answer
The file size of a digital audio file can be calculated using the following formula:
`File Size = Sample Rate × Duration × Sample Resolution`
1. **Identify the given values:**
* Sample Rate = 40,000 Hz
* Duration = 50 seconds
* Sample Resolution = 2 bytes per sample
2. **Calculate the file size in bytes:**
File Size (bytes) = 40,000 × 50 × 2
File Size (bytes) = 2,000,000 × 2
File Size (bytes) = 4,000,000 bytes
3. **Convert the file size from bytes to megabytes (MB):**
For GCSE, it is standard to use the conversion 1 MB = 1,000 KB = 1,000,000 Bytes.
File Size (MB) = 4,000,000 / 1,000,000
File Size (MB) = 4 MB.
Common mistakes
✗ Forgetting one of the components in the multiplication (e.g., duration).
✗ Using bits instead of bytes for the sample resolution without converting.
✗ Making an error in the conversion from bytes to megabytes (e.g., dividing by 1000 only once).
Practice the full AQA GCSE Computer Science Paper 2
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