A musician is looking to digitise a song from their record collection and is trying to establish how much space the sound file will take up on a portable hard drive. For recording the sound file, they are looking to use a sampling rate of 44 kHz with each sample being 4 bytes, initially on a single channel (mono).i.How many bits are there in each sample?ii.How many bits per second are processed while the music is being recorded? Express your answer in scientific notation to 3 significant figures.iii.The piece of music is 6 minutes and 20 seconds long. How many bits are processed in total? Express your answer in scientific notation to 3 significant figures.iv.If the sampling rate is increased to 128 kHz, how many bits will be processed using the same piece of music? Express your answer in scientific notation to 3 significant figures.v.What is the percentage increase in the number of bits processed as a result of increasing the sampling rate from 44 kHz to 128 kHz? Express your answer to the nearest percent.vi.After increasing the sampling rate, what would be the result of producing the sound file over two channels (stereo)? Express your answer in scientific notation to 3 significant figures.
Question
A musician is looking to digitise a song from their record collection and is trying to establish how much space the sound file will take up on a portable hard drive. For recording the sound file, they are looking to use a sampling rate of 44 kHz with each sample being 4 bytes, initially on a single channel (mono).i.How many bits are there in each sample?ii.How many bits per second are processed while the music is being recorded? Express your answer in scientific notation to 3 significant figures.iii.The piece of music is 6 minutes and 20 seconds long. How many bits are processed in total? Express your answer in scientific notation to 3 significant figures.iv.If the sampling rate is increased to 128 kHz, how many bits will be processed using the same piece of music? Express your answer in scientific notation to 3 significant figures.v.What is the percentage increase in the number of bits processed as a result of increasing the sampling rate from 44 kHz to 128 kHz? Express your answer to the nearest percent.vi.After increasing the sampling rate, what would be the result of producing the sound file over two channels (stereo)? Express your answer in scientific notation to 3 significant figures.
Solution
i. Each sample is 4 bytes. Since 1 byte = 8 bits, each sample is 4 * 8 = 32 bits.
ii. The sampling rate is 44 kHz, which means 44,000 samples are taken per second. Since each sample is 32 bits, the number of bits processed per second is 44,000 * 32 = 1.408 * 10^6 bits per second.
iii. The piece of music is 6 minutes and 20 seconds long, which is 380 seconds. The total number of bits processed is 1.408 * 10^6 bits/second * 380 seconds = 5.35 * 10^8 bits.
iv. If the sampling rate is increased to 128 kHz, the number of bits processed per second is 128,000 * 32 = 4.096 * 10^6 bits per second. The total number of bits processed for the same piece of music is 4.096 * 10^6 bits/second * 380 seconds = 1.56 * 10^9 bits.
v. The percentage increase in the number of bits processed as a result of increasing the sampling rate from 44 kHz to 128 kHz is ((1.56 * 10^9 - 5.35 * 10^8) / 5.35 * 10^8) * 100 = 192%.
vi. If the sound file is produced over two channels (stereo), the number of bits processed will be doubled. So, the total number of bits processed for the same piece of music is 2 * 1.56 * 10^9 = 3.12 * 10^9 bits.
Similar Questions
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Calculate how much storage space is needed to record a 32- bit, 7 khz, stereo music for a duration of 1 hour. (Give in bytes: put the value without symbol)Answer:
The piece of music is 6 minutes and 20 seconds long. How many bits are processed in total? Express your answer in scientific notation to 3 significant figures.
In digital audio, ----------------- describes the number of bits of information recorded for each sample.
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