How is the intensity in decibel computed?

[vijaygirish2001]

I use the Parselmouth's intensity = snd.to_intensity() function for computing the intensity. Can anyone let me know the formula/ expression for the intensity calculation function, and the frame size used?

I see intensity in decibel is computed as:

10 log(Mean energy/ Constant)

where Mean energy is frame level energy, I assume default frame size is 40 ms

If my assumption about the above expression is correct, what is the value of Constant used ?

[YannickJadoul]

Hi, @vijaygirish2001. Yes, the threshold is 4.0e-10 (or 2.0e-5 squared). The relevant part of Praat's code is here:

Parselmouth/praat/fon/Sound_to_Intensity.cpp

Lines 115 to 120 in 6111e6e

	const double intensity_in_Pa2 = double (sumxw / sumw);
	constexpr double hearingThreshold_in_Pa = 2.0e-5;
	constexpr double hearingThreshold_in_Pa2 = sqr (hearingThreshold_in_Pa);
	const double intensity_re_hearingThreshold = intensity_in_Pa2 / hearingThreshold_in_Pa2;
	const double intensity_in_dB_re_hearingThreshold = ( intensity_re_hearingThreshold < 1.0e-30 ? -300.0 :
	10.0 * log10 (intensity_re_hearingThreshold) );

The Praat manual also very shortly describes it here: https://www.fon.hum.uva.nl/praat/manual/Intensity.html. And details about the window size and time step are here: https://www.fon.hum.uva.nl/praat/manual/Sound__To_Intensity___.html.
https://www.fon.hum.uva.nl/praat/manual/sound_pressure_calibration.html discusses how these values are to some degree arbitrary for recorded audio, though, and how Praat interprets the amplitude values of the audio file as pressure values.