Question

A DJ has created a playlist for an event. She used a sampling rate of

2,000Hz and a sample resolution of 4 bits to record each audio file.
What is the minimum file size she will need to store a 15-second file
recording? Your answer should be in bytes and make sure you only
use numbers.

Answer 1

To calculate the minimum file size for a 15-second audio recording with a 2,000Hz sampling rate and 4-bit sample resolution, multiply the total samples (30,000) by the size per sample (0.5 bytes), resulting in a file size of 15,000 bytes.

Step-by-step explanation:

To calculate the file size of the audio recording, first, determine the total number of samples in the recording. Multiply the sampling rate by the duration of the audio:

• Sampling Rate: 2,000 samples per second
• Duration: 15 seconds

Total Samples = 2,000 samples/second × 15 seconds = 30,000 samples

Next, calculate the size per sample using the sample resolution:

• Sample Resolution: 4 bits

Since there are 8 bits in 1 byte, you need to convert the 4 bits into bytes:

Size per Sample = 4 bits/sample ÷ 8 bits/byte = 0.5 bytes/sample

Finally, calculate the minimum file size required to store the recording by multiplying the total samples by the size per sample:

Minimum File Size = Total Samples × Size per Sample = 30,000 samples × 0.5 bytes/sample = 15,000 bytes