sound pressure level

Air pressures are measured in Pascal (Pa), which are Newtons per square metre (N/m2). The ambient air pressure is about 100,000 Pa, and the lungs modify this in phonation only by a small amount, namely 200 to 1000 Pa (= 2 to 10 cm H2O). Outside your body, the air pressures caused by your speech are much smaller again, namely 0.01 to 1 Pa at 1 metre from your lips. These are comparable to the values that you see for a typical speech recording in Praat's sound window, although these numbers in Praat can be interpreted as true air pressures only if you perform a sound pressure calibration (including the multiplication).

A normative human ear can detect a root-mean-squared air pressure as small as 0.00002 Pa, for a sine wave with a frequency of 1000 Hz. The sound pressure level can be expressed in dB relative to this normative threshold:

SPL = 10 log10 { 1/(t2-t1) ∫t1t2 x2(t) dt / (2·10-5 Pa)2 }

where x(t) is the sound pressure in Pa as a function of time, and t1 and t2 are the times between which the energy (squared air pressure) is averaged. For a calibrated sound, Praat's sound window will show you the SPL as a function of time, if you switch on Show intensity and set its averaging method to energy (with Intensity settings...).

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© ppgb, November 24, 2004