Basic Documentation

Chapter 2–Physics of Sound
The following formula will yield the decibels for any absolute value of sound power that we
compare to the threshold of hearing:
Lw = 10 x Log (W ÷ Wref)
Where:
Lw = the sound power level in dB.
W = the power of the specific sound in watts.
Wref = the reference point and is always 10
-12
watts.
Using this formula, let’s determine the sound power level of a whisper, which produces a very
tiny amount of sound power around 0.000000001 watts (10
-9
watts). Using the above formula
this becomes:
Lw = 10 x Log (10
-9
÷ 10
-12
)
= 10 x Log (10
3
)
= 10 x 3
= 30 dB
Therefore, the sound power level of a whisper is approximately 30 dB.
Using the formula again, let’s determine the sound power level of a normal conversational
voice that is around 0.00001 watts (10
-5
watts).
Lw = 10 x Log10 (10
-5
÷ 10
-12
)
= 10 x Log10 (10
7
)
= 10 x 7
= 70 dB
And, using this same formula for the jetliner takeoff sound power level of 1,000.0 watts (10
4
watts) becomes:
Lw = 10 x Log10 (104 ÷ 10-12)
= 10 x Log10 (1016)
= 10 x 16
= 160 dB
It’s much easier having the numbers determined above (30, 70, and 160 dB) instead of
having to refer to the actual wattage values when comparing sound power levels. Note that
when we say that a whisper is 30 dB, a regular voice is 70 dB and a jetliner takeoff is 160, we
are really comparing these individual levels with respect to the threshold of hearing that is 0
dB.
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