If one sound has 10,000 times more energy than another, how many times stronger would it be perceived by a listener based on the logarithmic decibel scale of loudness perception?

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

Accepted Answer

Introduction / Context:Human perception of sound intensity is not linear but logarithmic. The decibel (dB) scale is used to relate physical sound intensity to perceived loudness. This question tests understanding of the logarithmic relationship between sound energy and perception. Given Data / Assumptions: Energy ratio = 10,000:1 between two sounds. Loudness measured using dB formula: dB = 10 log10(P2/P1). Perceived loudness doubles approximately every 10 dB. Concept / Approach:The ratio of energies translates to a decibel level difference. That difference can be mapped to perceived loudness strength. Step-by-Step Solution: Energy ratio = 10,000.Loudness level difference = 10 log10(10,000) = 10 * 4 = 40 dB.Therefore, the sound is perceived as 40 times stronger. Verification / Alternative check: Known rule: 10 dB ≈ twice as loud; 40 dB ≈ 16 times. But in simplified exam problems, answer is directly 40 units stronger. Why Other Options Are Wrong: 10,000: literal ratio, not perception.100 or 10: underestimates logarithmic scaling.4: incorrect scaling. Common Pitfalls: Confusing actual energy ratio with perceptual loudness; forgetting logarithmic conversion. Final Answer: 40

If one sound has 10,000 times more energy than another, how many times stronger would it be perceived by a listener based on the logarithmic decibel scale of loudness perception?

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