Question

if a large housefly\(3.0\;{\rm{m}}\)away from you makes a noise of\(40.0\;{\rm{dB}}\), what is the noise level of\(1000\)flies at that distance, assuming interference has a negligible effect?

Short answer

The intensity is \(70\;{\rm{dB}}\).

Step-by-step solution

Given Data

The loudness of the flyis \(d = 40.0\;{\rm{dB}}\).

The number of flies is \(n = 1000\).

The sound intensity and loudness

Sound intensity is the physical attribute of sound. Also, Loudness is the psychological correlate of intensity.

Calculation of the intensity

Use the intensity of the sound is,

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

So,

\(\begin{align}40.0 &= 10\log \frac{I}{{{{10}^{ - 12}}}}\\4 &= \log \frac{I}{{{{10}^{ - 12}}}}\\{10^4} &= \frac{I}{{{{10}^{ - 12}}}}\\I &= {10^{ - 8}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\end{align}\)

The net energy of the flies is,

\(nE = 1000E\).

We can write,

\({I_1} = \frac{E}{A}\)

Again,

\(\begin{align}{I_2} &= \frac{{1000E}}{A}\\ &= 1000{I_1}\\ &= 1000 \times {10^{ - 8}}\\ &= {10^{ - 5}}\;{\rm{W/}}{{\rm{m}}^{\rm{2}}}\end{align}\)

Calculation of the intensity level

The intensity level is,

\(\begin{align} &=10\log \frac{{{{10}^{ - 5}}}}{{{{10}^{ - 12}}}}\\ &= 10\log {10^7}\\ &= 70\;{\rm{dB}}\end{align}\)

Therefore,the noise level of\(1000\)flies at that distance is\(70\;{\rm{dB}}\), assuming interference has a negligible effect