# Decibel values: sum and difference

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Decibel values: sum and difference. Sound level summation in dB (1): Incoherent (energetic) sum of two different sounds: Lp 1 = 10 log (p 1 /p rif ) 2.

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Decibel values: sum and difference

Sound level summation in dB (1):
“Incoherent” (energetic) sum of two “different” sounds: Lp1 = 10 log (p1/prif)2 (p1/prif)2 = 10 Lp1/10 Lp2 = 10 log (p2/prif) (p2/prif)2 = 10 Lp2/10 (pT/prif)2 = (p1/prif)2 + (p2/prif)2 = 10 Lp1/ Lp2/10 LpT = Lp1 + Lp2 = 10 log (pT/prif)2 = 10 log (10 Lp1/ Lp2/10 )

Sound level summation in dB (2):
“incoherent” sum of two levels Example 1: L1 = 80 dB L2 = 85 dB LT= ? LT = 10 log (1080/ /10) = 86.2 dB. Example 2: L1 = 80 dB L2 = 80 dB  LT = 10 log (1080/ /10) = LT = log 2 = 83 dB.

Sound level subtraction in dB (3):
Level difference Example 3: L1 = 80 dB LT = 85 dB L2 = ? L2 = 10 log (1085/ /10) = dB

Sound level summation in dB (4):
“Coherent” sum of two (identical) sounds: Lp1 = 20 log (p1/prif) (p1/prif) = 10 Lp1/20 Lp2 = 20 log (p2/prif) (p2/prif) = 10 Lp2/20 (pT/prif) = (p1/prif)+ (p2/prif) = 10 Lp1/ Lp2/20 LpT = Lp1 + Lp2 = 10 log (pT/prif)2 = 20 log (10 Lp1/ Lp2/20 )

Level summation in dB (5):
“coherent” sum of levels Example 4: L1 = 80 dB L2 = 85 dB LT= ? LT = 20 log (1080/ /20) = 88.9 dB. Example 5: L1 = 80 dB L2 = 80 dB  LT = 20 log (1080/ /20) = LT = log 2 = 86 dB.