Discussion
Calculate the resultant noise of four machines emitting the equal sound level of 60 dB(A) :
Answer: D
The combined level is 66 dB(A).
Decibels are logarithmic, so sound levels add as energies, not as numbers. For n equal sources each at level L:
\[ \begin{aligned} L_{total} &= L + 10\log_{10} n \\ &= 60 + 10\log_{10} 4 \\ &= 60 + 6.02 \approx 66\ \text{dB(A)} \end{aligned} \]
Each doubling of identical sources adds 3 dB: two machines give 63 dB(A) and four give 66 dB(A). 120 dB(A) is what adding the decibels arithmetically gives for just two machines, and 90 dB(A) also treats the decibel scale as linear; both overstate the increase. 63 dB(A) is the answer for only two machines.
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