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Decibel values: sum and difference

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 (p 1 / p rif ) 2 = 10 Lp1/10 Lp 2 = 10 log ( p 2 /p rif ) 2 ( p 2 /p rif ) 2 = 10 Lp2/10

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Decibel values: sum and difference

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  1. Decibel values: sum and difference

  2. 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)2 (p2/prif)2 = 10 Lp2/10 (pT/prif)2 = (p1/prif)2 + (p2/prif)2= 10 Lp1/10 + 10 Lp2/10 LpT= Lp1 + Lp2 = 10 log (pT/prif)2 = 10 log (10 Lp1/10 + 10 Lp2/10 )

  3. 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 + 1085/10) = 86.2 dB. • Example 2: • L1 = 80 dB L2 = 80 dB • LT = 10 log (1080/10 + 1080/10) = • LT = 80 + 10 log 2 = 83 dB.

  4. Sound level subtraction in dB (3): • Level difference • Example 3: • L1 = 80 dB LT = 85 dB L2 = ? • L2 = 10 log (1085/10 - 1080/10) = 83.35 dB

  5. 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 Lp1/20 + 10 Lp2/20 LpT= Lp1 + Lp2 = 10 log (pT/prif)2 = 20 log (10 Lp1/20 + 10 Lp2/20 )

  6. Level summation in dB (5): • “coherent” sum of levels • Example 4: • L1 = 80 dB L2 = 85 dB LT= ? • LT = 20 log (1080/20 + 1085/20) = 88.9 dB. • Example 5: • L1 = 80 dB L2 = 80 dB • LT = 20 log (1080/20 + 1080/20) = • LT = 80 + 20 log 2 = 86 dB.

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