Noise Pollution MCQ with answer and solution

Concept

Logarithmic addition of sound pressure levels

Formula

L_total = 10 × log10(10^L1/10 + 10^L2/10)

Step-by-step solution

1. Sound pressure levels are defined logarithmically: L = 10 × log10(P² / P_ref²). 2. For two incoherent identical sources of level L, total level is L_total = 10 × log10(10^L/10 + 10^L/10). 3. This simplifies to L_total = L + 10 × log10(2) = L + 3.01 dB. 4. Substituting L = 70 dB yields 70 + 3 = 73 dB. Answer: B

Explanation

Decibels are logarithmic units, so acoustic sound pressure levels cannot be summed using simple arithmetic addition. Combining two independent, non-coherent sound sources of identical level (70 dB each) results in an exact increase of 3 dB above the individual source level, yielding a total sound pressure level of 73 dB.

Why the other options are wrong

A) 70 dB would indicate no acoustic addition from the second source. C) 76 dB corresponds to four identical 70 dB sources (a 6 dB increase). D) 140 dB represents linear arithmetic addition, ignoring the logarithmic decibel scale.

Shortcut

Doubling sound energy from two equal sources always adds exactly 3 dB.

Common mistake

Adding decibels arithmetically (70 + 70 = 140 dB) instead of logarithmically.