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

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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

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

More Questions from Measurements and Instrumentation

Discussion & Comments