When the intensity of sound is doubled, by how many decibels does the sound level increase?

Step-by-step solution

The sound level in decibels is given by the formula: L = 10 ₁₀ ( I I₀ ) When the intensity is doubled, the new intensity is I' = 2I . The new sound level is: L' = 10 ₁₀ ( 2I I₀ ) The increase in sound level is: L = L' - L = 10 ₁₀ ( 2I I₀ ) - 10 ₁₀ ( I I₀ ) L = 10 ₁₀ ( 2I / I₀ I / I₀ ) = 10 ₁₀(2) Substituting the value of ₁₀(2) 0.3010 : L = 10 0.3010 = 3.01 dB The sound level increases by approximately 3 dB .