Pulse code modulation (PCM) is used to encode live music as an uncompressed digital audio file - AQA - A-Level Physics - Question 3 - 2020 - Paper 8

The number of quantisation levels in a 16-bit encoding system is calculated using the formula $2^{n}$, where $n$ is the number of bits. Therefore, for 16 bits, the number of quantisation levels is $2^{16} = 65,536$.

To calculate the size of the digital file, we use the formula:

$\text{File Size} = \text{Duration (in seconds)} \times \text{Sampling Rate (Hz)} \times \text{Bit Depth} \times \text{Number of Channels}$

In this case:

• Duration: 3.5 minutes = 210 seconds
• Sampling rate: 44,100 Hz
• Bit depth: 16 bits
• Number of channels: 2 (stereo)

Thus, the file size in bits is:

$210 \times 44,100 \times 16 \times 2 = 2,943,000,000 \text{ bits}$

To convert this to megabytes:

$\text{File Size (MB)} = \frac{2,943,000,000}{8 \times 1,024 \times 1,024} \approx 348.93 \text{ MB}$

The music heard by the telephone caller will have lower quality compared to that of the original audio file from a compact disc. This is due to the limited bandwidth of 0.3 kHz – 3.4 kHz used for telephone calls, which cuts off higher frequencies, resulting in a loss of audio fidelity. In contrast, compact discs can reproduce a full audio range up to 20 kHz, allowing for richer sound and clarity.