Question Detail
Question
If the reference intensity (I₀) is 10⁻¹² W/m², what is the intensity level in decibels (dB) for a sound wave with an intensity (I) of 10⁻⁵ W/m²?
Correct Answer
Option C is the correct answer.
Detailed Explanation
The intensity level in decibels (L) is given by the formula L = 10 log₁₀ (I/I₀).Given I = 10⁻⁵ W/m² and I₀ = 10⁻¹² W/m².L = 10 log₁₀ (10⁻⁵ W/m² / 10⁻¹² W/m²) = 10 log₁₀ (10⁽⁻⁵ ⁻ ⁽⁻¹²⁾⁾) = 10 log₁₀ (10⁷).Since log₁₀(10⁷) = 7, L = 10 * 7 = 70 dB.
Hint
Use the formula for intensity level in decibels: L = 10 log₁₀ (I/I₀). Pay attention to the exponent rules for division of powers of 10.