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If the reference sound pressure P0 is 2 × 10^-5 N/m², what actual sound pressure corresponds to a sound level of 90 dB?

Difficulty: Medium

Correct Answer: 0.632 N/m²

Explanation:


Introduction / Context:
Sound levels in decibels (dB) are logarithmic measures of sound pressure relative to a reference level, usually 2 × 10^-5 N/m² in air. This question requires calculation of the actual sound pressure corresponding to 90 dB.


Given Data / Assumptions:

  • Reference sound pressure P0 = 2 × 10^-5 N/m².
  • Level Lp = 90 dB.
  • Formula: Lp = 20 log10(P / P0).


Concept / Approach:
Rearranging the formula: P = P0 × 10^(Lp/20). Substituting values gives the actual sound pressure. This is a standard conversion in acoustics.


Step-by-Step Solution:

Step 1: Lp = 90 dB.Step 2: P = 2 × 10^-5 × 10^(90/20).Step 3: 90/20 = 4.5.Step 4: 10^4.5 ≈ 31622.8.Step 5: P ≈ 2 × 10^-5 × 31622.8 ≈ 0.632 N/m².


Verification / Alternative check:

Checking unit consistency: Pressure remains in N/m². Calculation matches published sound pressure levels.


Why Other Options Are Wrong:

0.707, 0.835, and 0.925 are close but incorrect approximations.0.500 is significantly below the correct value.


Common Pitfalls:

Forgetting to divide by 20 (instead of 10) in the formula for pressure levels.


Final Answer:

0.632 N/m²
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