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I know that to calculate sound pressure level (db SPL) is

20 * log10 (amplitude)

but what I don't understand here is the range of the value. in case 16 bit signed PCM audio, the lowest value is -90 and the largest value is 0 :

[20 * log10 (1/32768)] to [20 * log10 (32768/32768)]  
[-90] to [0]

but per wikipedia, 0 is the lowest sound we can heard and 194 db SPL is something like shockwave sound. Could anybody explain what I'm missing here?

Thanks

user430926
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1 Answers1

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A digital waveform is a sampled and quantized representation of an analog electric signal. It just carries the original waveform numerically. While the analog electric signal isn't heard by itself either -- it needs to be transformed into an acoustic wave by means of transducers (e.g. speakers). The level of the acoustic pressure created by speakers depends on the capabilities of the speakers and the power amplifier. Different speakers / amplifier pairs driven by the same analog electric signal will produce different levels of acoustic pressure. The SPL decibels measure this acoustic pressure.

The analog electrical waveform as well as its digital representation decodes just a relative level of signal. And the 90 dB range you have calculated is called Signal to Noise Ratio (SNR), which is expressed in dimensionless dB, as this is a ratio; see https://en.wikipedia.org/wiki/Signal-to-noise_ratio

Mikhail Naganov
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