The GATE Grind

GATE 2025 AG – Question 21

Farm Power · Tractors and Power Tillers · 1 mark · Multiple choice

Tripling RMS sound pressure increases the sound-pressure level by approximately how many dB?

  1. 9.54
  2. 6.02
  3. 4.77
  4. 3.01

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Correct answer: (A) 9.54

Explanation

Sound-pressure level is $L_p=20\log_{10}(p_{rms}/p_{ref})$. Taking the difference cancels the reference: $\Delta L_p=20\log_{10}(3)=9.5424$ dB. Thus **9.54,A**. The factor is 20 for pressure amplitude, rather than the factor 10 used for an energy ratio.

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