Question

What sound intensity level in dB is produced by earphones that create an intensity of \(4.00 \times {10^{ - 12}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\)?

Short answer

The intensity level is \(86.0\;{\rm{dB}}\).

Step-by-step solution

Given Data

The intensity is \(I = 4.00 \times {10^{ - 12}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\).

The Measurement of Loudness

The loudness is an effect of the intensity of sound. The intensity generates from the amplitude of the sound wave. Loudness depends on the ratio of the sound intensity with the threshold sound.

Calculation of the intensity level

The intensity level of the sound is,

\({\rm{dB}} = 10\log \frac{I}{{{{10}^{ - 12}}}}\)

Substituting the values we get,

\(\begin{align}dB &= 10\log \frac{{4.00 \times {{10}^{ - 12}}}}{{{{10}^{ - 12}}}}\\ &= 86.0\;{\rm{dB}}\end{align}\)

The sound intensity level in dB is \(86.0\;{\rm{dB}}\)