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 = I₁²/I₀.What is the new decibel level? A)2.0 B)20 C)100 D)it will square the decibel level

Question

Quizplus · Accepted Answer

The decibel level is given by the formula:

dB = 10 log10(I/I0)

where I is the intensity of the sound, I0 is the threshold of hearing, and log10 is the base-10 logarithm.

Taking the ratio of the new intensity to the threshold, we get:

(I/I0) = (I11/I10) * (I12/I11)

= S1U1P1

Taking the logarithm of this ratio, we get:

log10 (I/I0) = log10 (S1U1P1)

Plugging this into the decibel formula, we get:

dB = 10 log10 (S1U1P1)

= 10 * 1

= 10

So the new decibel level is 10 dB.

Therefore, the 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