Question

As far as I know when I load wav files to matlab with command:

song = wavread('file.wav');

array song have elements with values from -1 to 1. This file (and hardware) is prepared to be played with 80dB. I need to add +30dB to achieve 110dB.
I do +10dB by multiplying by sqrt(10), so to get +30dB I do:

song = song*10*sqrt(10); which is the same as

song = song*sqrt(10)*sqrt(10)*sqrt(10);

Now values of array song have much greater values than -1 to 1 and I hear distorted sound.
Is it because of this values greater than <-1,1> or quality of my speakers/headphones?

Answer 1

The distortion is because your values are exceeding +/-1. The float values are converted to ADC counts, which are either +/-32768 (for a 16-bit ADC) or +/-8388608 (for a right-justified 24-bit ADC) or +/-2147483648 (for a left-justfied 24-bit ADC). For a 16-bit ADC, this is usually accomplished by an operation like adcSample = (short int)(32768.0*floatSample); in C. If floatSample is > +1 or < -1 this will cause wraparound in the short int cast, which is the distortion you hear. The cast is necessary because the ADC expects 16-bit digital samples.

You will need to adjust your amplifier/speaker settings to get the sound level you desire.

Conversely, you could create a copy of your file, lower it by 30 dB, adjust your amplifier/speakers to play the new file at 80 dB, then play the original file at the same amp/speaker settings. This will cause the original file to be played at 110 dB.

As Paul R noted in his comment, I am guessing here that you are using dB as shorthand for dB SPL when referring to the actual analog sound level produced by the full signal chain.