Tyco 579-769 Equation 2-5. dB and Sound Pressure Levels, Equation 2-6. Adding Decibels

Basic Audio Math, Continued

Ohm’s Law

and the Decibel, (continued)

Adding Decibels

When the decibel is used to express SPL, the reference sound pressure is 20 x 10-6Newtons/m² which is approximately the threshold for hearing for a normal listener. When using a dB meter to measure sound, the meter is performing the calculation between the received SPL and the reference SPL:

	⎛	SPL	⎞
dB	= 20log⎜		⎟
		20⋅10−6
spl	⎝		⎠

Equation 2-5. dB and Sound Pressure Levels

When multiple sound sources are combined, there is an increase in SPL. However, you cannot

add decibels directly:

90 dB + 90 dB is not 180 dB but 93 dB. Doubling the power results in a +3 dB SPL increase. To add SPL decibels:

1.Convert the decibels back to the original power value (which for SPL, is referenced to 1pW or 10-12W).

2.Add the numbers together.

3.Convert the numbers back to decibels.

To add 90 dB + 90 dB:

⎛

P

⎞

−12

dB = 10 log

⎜

⎟

;

P

=

1 pW =

10

W

⎜

⎟

0

⎝ P0

⎠

⎛

P

⎞

90 = 10 log ⎜

⎟

⎝ 10−12

⎠

⎛

P

⎞

⎛

P

⎞

9 = log ⎜

⎟ ;

109 = ⎜

⎟

−

−

⎝

10

12

⎠

⎝

10 12

⎠

P= (109)(10−12)= (10−3) = 0.001 W 2P = 2 x 0.001 W = 0.002 W

⎛ 0.002		⎞	= 93
dB = 10 log ⎜	10−12	⎟
⎝		⎠

Equation 2-6. Adding Decibels

2-3