Discussion
What is the resultant noise if 8 sound levels of 50 dB(A) each mixed together ?
Answer: C
The resultant level is 59 dB(A).
Decibels add logarithmically. For n equal sources each of level L:
\[ \begin{aligned} L_{total} &= L + 10\log_{10} n \\ &= 50 + 10\log_{10} 8 \\ &= 50 + 9.03 \approx 59\ \text{dB(A)} \end{aligned} \]
Each doubling of identical sources adds 3 dB: two sources give 53, four give 56 and eight give 59. So 53 and 56 dB(A) are the levels for two and four sources, and 60 dB(A) would need ten.
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