If the reference sound pressure P0 is 2 × 10^-5 N/m², what actual sound pressure corresponds to a sound level of 90 dB?
Electronics and Communication Engineering
Measurements and Instrumentation
Difficulty: Medium
Choose an option
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A0.632 N/m²
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B0.707 N/m²
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C0.835 N/m²
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D0.925 N/m²
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E0.500 N/m²
Answer
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