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Why is a WAV file created from a .mp3 file so much larger?

It is well known that .wav is the format used for uncompressed audio files. On the other hand, .mp3 files are usually the result of audio files after compression. For example, during compression, only the larger of the two tones that are too close in frequency are saved (so that they mask each other). In addition, quantization noise is introduced in parts of the time or frequency spectrum that are not perceptually important (for example, frequencies that are too high or too low). It is clear that a lot of (perceptually) redundant information is discarded, which reduces file size.

My question : why is the WAV file obtained from .mp3 much larger than the .mp3 file? From the theoretical informational representation of the additional information related to the song was not added, so why the increase in size? Is this just a consequence of how the data is stored in .wav format? Any answers / links would be greatly appreciated. Thanks!

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The way the two audio stores differ at night and day. Simply put, a WAV file (which is PCM audio) stores much more data than an MP3 file.

Sound PCM measures the pressure on each sample. There are many patterns. Audio CD quality uses 44,100 samples per second per channel. The red lines here are patterns:

enter image description here

Graph from: http://en.wikipedia.org/wiki/Sampling_rate

MPEG-1 Layer 3 (and many other lossy audio compression codecs) use a different audio encoding method. Instead of measuring pressure over time, they measure the frequency components over time. MP3 encoders determine which frequencies are present in a signal for a short period of time called a frame. A frame can be 576 samples or so long. For these samples, they reproduce a set of frequencies.

Now all this is too simplified. There are many good tricks in MP3 to filter out frequencies that will be masked by others, and some nice smoothing of the playback so that it sounds close to the original.

You can find my answer here in more detail: https://video.stackexchange.com/a/635/129

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