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GATE 2024 ES – Question 58

Air and Noise Pollution · Noise Pollution · 2 marks · Numerical answer

Adjacent noise sources have levels30 and 40 dB. Find combined level in dB, to two decimals. Reference pressure is 20 µPa.

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Correct answer: 40.00 to 41.00

Explanation

For independent, incoherent sources, add mean-square pressures, not pressure amplitudes or dB values. $$L=10\log_{10}(10^{30/10}+10^{40/10})=10\log_{10}(11000)=40.413927.$$ Answer **40.41 dB**. The common reference pressure cancels in this logarithmic addition; phase-coherent sources would require phase information.

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