Question Detail
Question
The loudness in decibels (L) is given by L = 10 log₁₀(I/I₀), where the reference intensity I₀ = 10⁻¹² W/m². If a sound intensity I is measured to be 10⁻¹⁰ W/m², what is its loudness in decibels?
Correct Answer
Option B is the correct answer.
Detailed Explanation
Using the formula L = 10 log₁₀(I/I₀) from page 19: L = 10 log₁₀(10⁻¹⁰ W/m² / 10⁻¹² W/m²) = 10 log₁₀(10⁻¹⁰ / 10⁻¹²) = 10 log₁₀(10⁻¹⁰ ⁺ ¹²) = 10 log₁₀(10²). Since log₁₀(10²) = 2, then L = 10 * 2 = 20 dB. This calculation method is demonstrated on page 19.
Hint
Apply the decibel formula L = 10 log₁₀(I/I₀) and use the properties of logarithms. The values for I and I₀ are given in the question and in the document.