Question

The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ? Use a calculator. Round to the nearest whole number.

Answer 1

The intensity of the sound, when I = 10^-9 W/m^2, is 30 dB.

Step-by-step explanation:

The equation to calculate the intensity of a sound in decibels (dB) is given by I(dB) = 10 * log10(I / I0), where I is the intensity of the sound and I0 is the threshold of hearing intensity.

To find the intensity, in decibels, when I = 10-9 W/m2, we substitute I = 10-9 and I0 = 10-12 into the equation:

I(dB) = 10 * log10((10-9) / (10-12))

I(dB) = 10 * log10(103)

I(dB) = 10 * 3

I(dB) = 30 dB

Therefore, the intensity of the sound, when I = 10-9 W/m2, is 30 dB.