Representing Sound

• Sample Rate: Measured in Hertz (Hz), this defines how many samples are taken per second. A higher sample rate allows the system to capture higher frequency sounds accurately, as it can track faster changes in the wave's shape.

• Sample Resolution (Bit Depth): This is the number of bits used to store each sample measurement. It determines the number of possible amplitude levels that can be recorded, which directly impacts the dynamic range and the precision of the volume levels.

• Mathematical Relationship: The number of available amplitude levels is calculated as $2^n$, where $n$ is the bit depth. For example, an 8-bit resolution provides $2^8 = 256$ possible levels, while 16-bit provides $65,536$ levels.

• The Formula: The total size of an uncompressed audio file is the product of the sampling frequency, the bit depth, and the duration of the recording. This calculation determines the storage space required for the raw data.

Core Formula: $\text{File Size (bits)} = \text{Sample Rate (Hz)} \times \text{Sample Resolution (bits)} \times \text{Duration (seconds)}$

• Step-by-Step Calculation: First, identify the rate in Hz and the resolution in bits. Multiply these by the total time in seconds to get the size in bits, then divide by $8$ to convert to bytes, and further by $1024$ or $1000$ to reach Kilobytes or Megabytes as required.

• Analogue vs. Digital: Analogue is continuous and theoretically infinite in detail but prone to interference. Digital is discrete and finite, which makes it easier to store and copy without degradation, though it is always an approximation of the original.

• Unit Consistency: Always ensure the duration is in seconds before calculating file size. If a question provides time in minutes, multiply by $60$ immediately to avoid massive calculation errors.

• Bits vs. Bytes: Examiners often ask for the answer in Bytes, Kilobytes (KB), or Megabytes (MB). Remember that $8 \text{ bits} = 1 \text{ Byte}$, and use the appropriate conversion factor ($1000$ or $1024$) specified in the exam board's requirements.

• Reasonableness Check: If a 10-second clip results in a file size of several Gigabytes, re-check your decimal places or unit conversions. Standard CD quality is roughly $10 \text{ MB}$ per minute; use this as a mental benchmark.

• Confusing Rate and Resolution: Students often think increasing the sample rate makes the sound 'louder' or 'clearer' in volume. In reality, the rate only affects the frequency accuracy, while the resolution affects the volume precision.

• The 'Perfect' Digital Wave: A common misconception is that digital sound is identical to analogue. It is important to remember that digital sound is always a 'staircase' approximation, even if the steps are too small for the human ear to detect.

• Ignoring Stereo: If a recording is in stereo, the file size calculation must be multiplied by $2$ because there are two independent channels of audio data being recorded simultaneously.