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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
Question 3
Pulse code modulation (PCM) is used to encode live music as an uncompressed digital audio file. Sampling of the analogue signal is carried out at 44.1 kHz. A 16-bit ... show full transcript
Worked Solution & Example Answer: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
Step 1
Explain why the sampling frequency used is suitable for this task.
Answer
The sampling frequency of 44.1 kHz is suitable for this task as it is at least twice the maximum frequency of the audio range, which is typically around 20 kHz. This follows the Nyquist theorem, which states that to accurately reproduce a signal, it must be sampled at a rate greater than twice its maximum frequency.
Step 2
Calculate the number of quantisation levels available on a 16-bit encoding system.
Answer
The number of quantisation levels is calculated using the formula:
where n is the number of bits. For a 16-bit encoding system, the calculation is:
Thus, there are 65,536 quantisation levels available.
Step 3
Calculate the size, in megabytes, of the digital file needed to store this recording.
Answer
To calculate the file size, we use the following formula:
ext{File size (MB)} = rac{ ext{Duration (seconds)} imes ext{Sampling Rate (Hz)} imes ext{Bit Depth} imes ext{Number of Channels}}{8 imes 1024 imes 1024}
Given:
- Duration = 3.5 minutes = 210 seconds
- Sampling Rate = 44.1 kHz = 44100 Hz
- Bit Depth = 16 bits
- Number of Channels = 2
Substituting the values:
ext{File size} = rac{210 imes 44100 imes 16 imes 2}{8 imes 1024 imes 1024}
Calculating:
\approx 37 ext{ megabytes} $$Step 4
Compare the quality of the music heard by the telephone caller with that of the original file heard when played directly from a compact disc.
Answer
The quality of the music heard by the telephone caller is lower than that of the original file played directly from a compact disc. This is due to the telephone network using a bandwidth of 0.3 kHz to 3.4 kHz, which limits the audio frequency range. In contrast, compact discs can reproduce audio frequencies up to 20 kHz, leading to a richer and more detailed sound experience. The loss of high and low frequencies will make the music sound less vibrant and clear over the telephone.