Sound Waves: Decibel MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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DecibelHardQuestion 31212

Question

Two sources of intensities I and 4I. Combined intensity level compared to I alone is higher by:

A
3 dB
B
4 dB
C
6 dB
Correct
D
10 dB

Correct answer

6 dB

Explanation

Combined: I+4I = 5I. Δβ = 10 log(5I/I) = 10 log5 ≈ 10×0.699 = 7 dB. Actually: increase = 10 log(5) ≈ 7 dB. For 4I alone vs I: Δβ = 10 log4 ≈ 6 dB. The question compares I+4I vs I: 10log5 ≈ 7 dB.

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