If I₀ = 10−¹² W/m² is the threshold of hearing,a sound with intensity I₁ = 10−¹¹ W/m² will give a certain decibel level.Suppose a new sound has an intensity I₂ = 2I₁²/I₀.What is the new decibel level? A)2.3 dB B)23 dB C)100 dB D)it will square the decibel level E)1.0 dB

Question

Quizplus · Accepted Answer

The sound intensity level (SIL) in decibels (dB) is given by SIL = 10log(I/I_0), where I is the sound intensity and I_0 is the threshold of hearing 10^(-12) W/m^2.

The initial sound has an intensity of I = 10^(-11) W/m^2, so its SIL is SIL1 = 10log(10^(-11)/10^(-12)) = 110 dB.

The new sound has an intensity of I' = 2I/10^(-12) = 2x10^(-11) W/m^2, so its SIL is SIL2 = 10log(2x10^(-11)/10^(-12)) = 120 dB.

Therefore, the change in decibel level is SIL2 - SIL1 = 120 dB - 110 dB = 10 dB, which is equivalent to a perceived doubling of loudness.

The closest answer choice is B, 23 dB, which is incorrect. Therefore, there is no exact match, and the closest answer is B.

If I0 = 10−12 W/m2 Is the Threshold of Hearing,a

If I₀ = 10−¹² W/m² Is the Threshold of Hearing,a