Respuesta :
Answer:
[tex]E=5.0662\times 10^{-3}\ J[/tex]
Explanation:
Given:
- time of exposure of eardrum to the specific sound, [tex]t=8\ hr=28800\ s[/tex]
- intensity of the sound, [tex]\beta=95\ dB[/tex]
- diameter of the eardrum, [tex]d=0.85\ cm=0.0085\ cm[/tex]
We have the relation between the flux density of the sound energy as:
[tex]\beta=10\log_{10}(\frac{I}{I_0} )[/tex] ................(1)
where:
[tex]I_0=[/tex] the minimum flux density of sound energy just audible to human ears [tex]=10^{-12}[/tex] [tex]W.m^{-2}[/tex]
[tex]I=[/tex] the flux density of the sound energy due to the given intensity of sound
[tex]\beta=[/tex] given intensity of sound in decibels
from eq. (1) we've:
[tex]95=10\times \log_{10} (\frac{I}{10^{-12}} )[/tex]
[tex]I=0.0031\ W.m^{-2}[/tex]
The above value is Power per unit area.
We now find the area of eardrum:
[tex]A=\frac{\pi.d^2}{4}[/tex]
[tex]A=\frac{\pi\times 0.0085^2}{4}[/tex]
[tex]A=5.67\times 10^{-5}\ m^2[/tex]
Now the energy reaching the eardrum per second is:
[tex]P=I\times A[/tex]
[tex]P=0.0031\times 5.67\times 10^{-5}[/tex]
[tex]P=1.7591\times 10^{-7}\ W[/tex]
Now the total energy reaching the eardrum in the given time:
[tex]E=P.t[/tex]
[tex]E=1.7591\times 10^{-7}\times 28800[/tex]
[tex]E=5.0662\times 10^{-3}\ J[/tex]
