Praxis Audiology (5343)

The decibel (dB) is a logarithmic ratio of a measured quantity to a reference. It compresses the enormous range of audible intensities (about 10¹² to 1 from threshold to pain) into a manageable scale of about 0 to 120–140 dB. Because it is a ratio, every dB value must specify its reference; a level without a reference is undefined.

Hearing level (HL) Level re audiometric zero

Level re listener's own threshold

Intensity is proportional to pressure squared, so the pressure formula uses 20 log and the intensity formula uses 10 log; both yield the same dB value for the same sound. Key ratios to memorize: doubling intensity = +3 dB; doubling pressure = +6 dB; 10 times pressure = +20 dB; 10 times intensity = +10 dB; 100 times pressure = +40 dB. A level of 0 dB means the measured value equals the reference, not the absence of sound; negative values mean the quantity is below the

HL, SPL, and SL in Practice dB HL is referenced to the average threshold of normal young adults at each frequency (audiometric zero), so the normal audiogram is flat at 0 dB HL even though the SPL needed for threshold varies with frequency (larger at 250 Hz than at 1000 Hz). dB SL is referenced to a particular listener's threshold for that stimulus. If a patient's SRT is 35 dB HL and word recognition is tested at 40 dB SL, the presentation level is 75 dB HL. dB nHL is used for brief stimuli such as clicks and is referenced to behavioral thresholds of normal listeners for that stimulus; dB peSPL (peak-equivalent SPL) describes a transient by the SPL of a sinusoid with the same peak amplitude.

Decibels cannot be added arithmetically. Uncorrelated (incoherent) sources such as two noise generators sum by intensity: L_total = 10 log (10^(L1/10) + 10^(L2/10)). Two equal sources add 3 dB; N equal sources add 10 log N (4 sources +6 dB, 10 sources +10 dB). When the levels differ, add a correction to the higher level that shrinks as the difference grows; once sources differ by more than about 10 dB, the weaker one contributes essentially nothing.

ADDING TWO INCOHERENT SOURCES dB added to higher level

Difference between the two levels (dB)

Coherent, in-phase identical signals add 6 dB (pressure doubling); 180 degrees out of phase they cancel.

Worked examples of the addition and subtraction rules follow.

Two machines at 85 and 85 dBA

Two machines at 90 and 86 dBA

Four identical sources, total must not exceed 40 dBA

Subtracting background noise

In a free field, intensity from a point source falls with the square of distance (I ∝ 1/r²), so level drops 6 dB per doubling of distance and 20 dB per tenfold increase: ΔL = 20 log (r1/r2). A talker producing 66 dB SPL at 1 m yields about 60 dB SPL at 2 m and about 54 dB SPL at 4 m. Moving a remote microphone from 2 m to 15 cm improves the signal by 20 log (2/0.15) ≈ 22.5 dB. In rooms, the law holds only within the critical distance; beyond it the reverberant field dominates and level stops falling, the rationale for remote-microphone systems in classrooms.