GATE 2026 ES – Question 47
Sound levels at urban locations A, B, C, D are 40,55,65,75 dBA. Find the average sound level in dBA, to two decimal places.
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Correct answer: 65 to 75
Explanation
Decibels represent a logarithm of acoustic energy; average the corresponding linear energies with equal weighting. $$L_{avg}=10\log_{10}\left[\frac{10^{40/10}+10^{55/10}+10^{65/10}+10^{75/10}}4\right]=69.43387\ldots.$$ Therefore **69.43 dBA**. An arithmetic mean of the four decibel numbers would not be the energy-average level.