# Understanding values saved in WAVE file

The values that one can find in a wave file, e.g.

    0.0036
0.0026
0.0174
0.0050
0.0026
0.0108
0.0154
-0.0114
-0.0006
0.0115


are - as I assume - relative values between -1 and 1, the range you normally see when watching a waveform in some audio editing program. Now, how are these relative values mapped when you playback a file? E.g. if there is a value of 0.5, does it mean playback at half of the maximal possible loudness? Is there some kind of reference value stored in the WAVE file to which the relative values refer to?

Another thing: In the example above there are 7 positive values follow by 2 negative values. So the membran vibrating in a speaker to create the sound is pressed longer in one direction than in the other direction, or how does one has to interpret this? Positive values are one direction of the vibration and negative ones are vibrations into another direction or am I wrong about this?

Thank you very much :-)

What you see are time-domain samples that correspond to the displacement of a speaker from some rest position as a function of time. For example, the first sample corresponds to the membrane's position at $t=0$, the next represents its position at $t=T$, and so on, assuming that there are $T$ seconds between samples. Common sampling intervals for audio include $T = \frac{1}{8000}$ sec and $T = \frac{1}{44100}$ sec.
As you noted, the sample values are normalized to a range of $\pm1$. The resulting loudness of the audio can be affected by many non-digital factors, such as the gain of the amplifier driving the speaker or the DAC's output voltage range. The peak sample values $\pm1$ just correspond to "maximum membrane displacement that the hardware can generate." Therefore, there is no way to encode absolute loudness of the audio in such a stream of samples, hence the use of such a normalization scheme.
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