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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

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

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Sound level summation in dB (2): incoherent sum of two levels Example 1: L 1 = 80 dB L 2 = 85 dB L T = ? L T = 10 log (10 80/10 + 10 85/10 ) = 86.2 dB. Example 2: L 1 = 80 dB L 2 = 80 dB L T = 10 log (10 80/10 + 10 80/10 ) = L T = 80 + 10 log 2 = 83 dB.

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Sound level subtraction in dB (3): Level difference Example 3: L 1 = 80 dB L T = 85 dB L 2 = ? L 2 = 10 log (10 85/10 - 10 80/10 ) = 83.35 dB

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Sound level summation in dB (4): Coherent sum of two (identical) sounds: Lp 1 = 20 log (p 1 /p rif )(p 1 /p rif ) = 10 Lp1/20 Lp 2 = 20 log (p 2 /p rif ) (p 2 /p rif ) = 10 Lp2/20 (p T /p rif ) = (p 1 /p rif )+ (p 2 /p rif ) = 10 Lp1/20 + 10 Lp2/20 Lp T = Lp 1 + Lp 2 = 10 log (p T /p rif ) 2 = 20 log (10 Lp1/20 + 10 Lp2/20 )

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Level summation in dB (5): coherent sum of levels Example 4: L 1 = 80 dB L 2 = 85 dB L T = ? L T = 20 log (10 80/20 + 10 85/20 ) = 88.9 dB. Example 5: L 1 = 80 dB L 2 = 80 dB L T = 20 log (10 80/20 + 10 80/20 ) = L T = 80 + 20 log 2 = 86 dB.

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