Answer:
10,109 songs
Step-by-step explanation:
To calculate the storage required for one song, we need to consider its audio characteristics and compression ratio:
1. Sampling Rate: 44,100 samples per second
2. Bit Depth: 16 bits
3. Compression Ratio: 10:1
First, let's find out the storage size of the audio data without compression:
Sampling Rate * Bit Depth = Total bits per second
44,100 samples/second * 16 bits/sample = 705,600 bits/second
Since a song is 3 minutes long:
Total bits per song = 705,600 bits/second * 3 minutes * 60 seconds/minute = 126,720,000 bits
Next, we need to consider the compression ratio. With a compression ratio of 10:1, the size of the audio file will be reduced by a factor of 10.
So, the compressed size of one song = 126,720,000 bits / 10 = 12,672,000 bits
Now, we need to convert bits to bytes:
1 byte = 8 bits
Compressed size of one song in bytes = 12,672,000 bits / 8 bits/byte = 1,584,000 bytes
Now, we can find out how many songs can be stored on the available 16 GB storage:
16 GB = 16 * 1024 * 1024 * 1024 bytes
Number of songs = (16 * 1024 * 1024 * 1024 bytes) / (1,584,000 bytes/song)
Number of songs ≈ 10,109 songs
Therefore, approximately 10,109 songs can be stored on your smartphone.
